{"id":27503,"date":"2023-04-14T05:02:48","date_gmt":"2023-04-14T05:02:48","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=27503"},"modified":"2024-02-05T15:23:48","modified_gmt":"2024-02-05T15:23:48","slug":"area-of-an-equilateral-triangle-formula-derivation-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-equilateral-triangle","title":{"rendered":"Area of an Equilateral Triangle &#8211; Formula, Derivation, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-37da2e65-9028-4c42-90c0-19026ca2b532\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-equilateral-triangle#0-what-is-the-area-of-an-equilateral-triangle>What Is the Area of an Equilateral Triangle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-equilateral-triangle#1-area-of-an-equilateral-triangle-formula>Area of an Equilateral Triangle Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-equilateral-triangle#7-properties-of-equilateral-triangle>Properties of Equilateral Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-equilateral-triangle#9-solved-examples-on-area-of-equilateral-triangle>Solved Examples on Area of Equilateral Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-equilateral-triangle#10-practice-problems-on-area-of-equilateral-triangle>Practice Problems on Area of Equilateral Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-equilateral-triangle#11-frequently-asked-questions-on-area-of-equilateral-triangles>Frequently Asked Questions on Area of Equilateral Triangles<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-area-of-an-equilateral-triangle\">What Is the Area of an Equilateral Triangle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Area of an equilateral is the region bounded within the three sides of the triangle.<\/strong> In other words, the area of an equilateral triangle is the total region enclosed within the boundary of the triangle. It is calculated using the simple formula $\\frac{\\sqrt{3}}{4} \\times a^2$, where \u201ca\u201d is the length of the side.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An equilateral triangle is a triangle in which all sides are equal and all interior angles are congruent. Each angle of an equilateral triangle measures $60^\\circ$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"422\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/an-equilateral-triangle-abc.png\" alt=\"An equilateral triangle ABC\" class=\"wp-image-33819\" title=\"An equilateral triangle ABC\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/an-equilateral-triangle-abc.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/an-equilateral-triangle-abc-300x204.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the equilateral triangle ABC shown below, the area of the triangle is the green shaded region.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"459\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/area-of-an-equilateral-triangle.png\" alt=\"Area of an equilateral triangle\" class=\"wp-image-33820\" title=\"Area of an equilateral triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/area-of-an-equilateral-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/area-of-an-equilateral-triangle-300x222.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-to-find-the-area\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_find_area_pt.png\" alt=\"Add to Find the Area Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add to Find the Area Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/answer-questions-related-to-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_side_pt.png\" alt=\"Answer Questions Related to Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Answer Questions Related to Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-of-composite-figure\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_grannys_rescue_10_gm.png\" alt=\"Area of Composite Figure Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area of Composite Figure Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-with-unit-squares-and-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_unit_sq_side_length_pt.png\" alt=\"Area with Unit Squares and Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area with Unit Squares and Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-word-problems-on-product-of-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_real_life_prob_area_pt.png\" alt=\"Area Word Problems on Product of Fractions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area Word Problems on Product of Fractions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/build-the-area\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_grannys_rescue_3_4_5_gm.png\" alt=\"Build the Area Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Build the Area Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles-and-rectangles-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_2_pt.png\" alt=\"Classify Triangles and Rectangles as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles and Rectangles as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_triangles_pt.png\" alt=\"Classify Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/determine-the-area-of-rectilinear-shapes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_rectilinear_shapes_pt.png\" alt=\"Determine the Area of Rectilinear Shapes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Determine the Area of Rectilinear Shapes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-area-by-multiplying-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_multi_side_length_1_pt.png\" alt=\"Find Area by Multiplying Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Area by Multiplying Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = 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slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-area-of-an-equilateral-triangle-formula\">Area of an Equilateral Triangle Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula for area of equilateral triangle is given by:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area = \\frac{\\sqrt{3}}{4}\\times(a)^2$ square units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">where a is the length of the side of an equilateral triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"393\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/area-of-an-equilateral-triangle-formula.png\" alt=\"Area of an equilateral triangle formula\" class=\"wp-image-33821\" title=\"Area of an equilateral triangle formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/area-of-an-equilateral-triangle-formula.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/area-of-an-equilateral-triangle-formula-300x190.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the given triangle $ABC,\\; AB = BC = CA = a$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of $\\Delta ABC = \\frac{\\sqrt{3}}{4}\\times(a)^2$<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-fractions-using-area-models.jpeg\" alt=\"Add Fractions using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-like-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-like-fractions-using-area-models.jpeg\" alt=\"Add Like Fractions using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-mixed-numbers-and-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-mixed-numbers-and-fractions-using-area-models.jpeg\" alt=\"Add Mixed Numbers and Fractions using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-fractions-using-area-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/compare-fractions-using-area-model.jpeg\" alt=\"Compare Fractions Using Area Model Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-the-area-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/complete-the-area-model.jpeg\" alt=\"Complete the Area Model Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-the-equation-for-the-area-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/complete-the-equation-for-the-area-model.jpeg\" alt=\"Complete the Equation for the Area Model Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/convert-mixed-numbers-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/convert-mixed-numbers-using-area-models.jpeg\" alt=\"Convert Mixed Numbers Using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/create-area-models-to-multiply-unit-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t   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Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-how-to-find-the-area-of-an-equilateral-triangle\">How to Find the Area of an Equilateral Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find the area of an equilateral triangle, simply substitute the length of the side in the following formula:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area = \\frac{\\sqrt{3}}{4}\\times(a)^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Simplify and give the appropriate unit.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example: Find the area of an equilateral triangle side of 4 units.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Side = a = 4$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of an equilateral triangle $= \\frac{\\sqrt{3}}{4}\\times(a)^2 = \\frac{\\sqrt{3}}{4}\\times(4)^2 = 4\\sqrt{3}$ square units<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-derivation-of-area-of-an-equilateral-triangle-formula\">Derivation of Area of an Equilateral Triangle Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">All the sides are equal and all the internal angles are 60\u00b0 in an equilateral triangle. The formula to calculate the area of an equilateral triangle is given as,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Area of an equilateral triangle <\/strong>$= \\frac{\\sqrt{3}}{4}\\times(a)^2$ square units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">where,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a =$ Length of each side of an equilateral triangle<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can derive the above formula to find the area of an equilateral triangle in the following three ways.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-using-height\">Using Height<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find the area of any triangle, we require the length of the base and the height, since the general formula is:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Area of Triangle <\/strong>$= 12\\times$<strong> base <\/strong>$\\times$<strong> height<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"611\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/an-equilateral-triangle-with-side-a-and-height-h.png\" alt=\"An equilateral triangle with side a and height h\" class=\"wp-image-33822\" title=\"An equilateral triangle with side a and height h\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/an-equilateral-triangle-with-side-a-and-height-h.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/an-equilateral-triangle-with-side-a-and-height-h-300x296.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Calculating the height<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">First, we will calculate the height of an equilateral triangle in terms of the side length.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the right triangle ABD:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hypotenuse $= AB = a$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Base $= BD = \\frac{a}{2}$ units<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"437\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/the-height-of-the-equilateral-triangle.png\" alt=\"The height of the equilateral triangle\" class=\"wp-image-33823\" title=\"The height of the equilateral triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/the-height-of-the-equilateral-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/the-height-of-the-equilateral-triangle-300x211.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Based on Pythagoras\u2019 Theorem<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$AB^2 = BD^2 + AD^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a^2 = \\frac{a^2}{4} + AD^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$AD^2 = a^2\\;-\\;\\frac{a^2}{4} = \\frac{4a^2 &#8211; a^2}{4} = \\frac{3a^2}{4} = \\frac{\\sqrt{3a}}{2}$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Height $= h = \\frac{3a}{2}$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Area of Triangle<\/strong> $= 12\\times$<strong> base <\/strong>$\\times$ <strong>height<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substitute the value of base and height in the formula<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of equilateral triangle with height $\\frac{\\sqrt{3}a}{2}$ and base \u201ca\u201d can be given as&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area = \\frac{1}{2} \\times a \\times \\frac{\\sqrt{3}a}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Area of Equilateral Triangle <\/strong>$= \\frac{\\sqrt{3}a^2}{4}$<strong> square units<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-using-herons-formula\">Using Heron&#8217;s Formula<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When the lengths of the three sides of the triangle are known, Heron&#8217;s formula is used to find the area of a triangle.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"401\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/an-equilateral-triangle-with-sides-a-units.png\" alt=\"An equilateral triangle with sides \u201ca\u201d units\" class=\"wp-image-33824\" title=\"An equilateral triangle with sides \u201ca\u201d units\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/an-equilateral-triangle-with-sides-a-units.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/an-equilateral-triangle-with-sides-a-units-300x194.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider a triangle ABC with sides a, b, and c.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>The Heron&#8217;s formula<\/strong> to find the area of the triangle is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\\Area of a triangle $= \\sqrt{s (s &#8211; a) (s &#8211; b) (s &#8211; c)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Where,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">s is the semi-perimeter.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$s = \\frac{a + b + c}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For equilateral triangle: $a = b = c$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$s = \\frac{a + a + a}{2} = \\frac{3a}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, Area of equilateral triangle $= \\sqrt{\\frac{3a}{2}(\\frac{3a}{2}\\;-a)(\\frac{3a}{2}\\;-a)(\\frac{3a}{2}\\;-a)}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of equilateral triangle $= \\sqrt{\\frac{3a}{2}\\times\\frac{a}{2}\\times\\frac{a}{2}\\times\\frac{a}{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Area of equilateral triangle <\/strong>$= \\frac{\\sqrt{3}a^2}{4}$<strong> square units<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"6-using-two-sides-and-included-angle-sas-formula\">Using Two Sides and Included Angle (SAS) Formula<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">How are the angles of an equilateral triangle related to its area? If two sides and the included angle between two sides is known, we use the following variations to find the area of a triangle. There are three ways to use the same formula based on which side and included angle are given.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When sides \u201ca\u201d and \u201cb\u201d and the included angle C is known, the area of the triangle is: $Area = \\frac{1}{2} \\times ab \\times sin C$<br><\/li>\n\n\n\n<li class=\"eplus-wrapper\">When sides \u201cb\u201d and \u201cc\u201d and included angle A is known, the area of the triangle is: $Area = \\frac{1}{2} \\times bc \\times sin\\; A$<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When sides \u201ca\u201d and \u201cc\u201d and included angle B is known, the area of the triangle is: Area $= \\frac{1}{2}\\times ac \\times sin\\; B$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider an equilateral triangle ABC with sides a, b, and c.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">What are the angles of an equilateral triangle? Each interior angle A, B, and C measures $60^\\circ$. Thus, $\\angle A = \\angle B = \\angle C = 60^\\circ$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow sin\\; A = sin\\; B = sin\\; C$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Also, for an equilateral triangle, $a = b = c$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of $\\Delta ABC = \\frac{1}{2}\\times b \\times c \\times sin\\;(A) = \\frac{1}{2} \\times a \\times b \\times sin\\; (C) = \\frac{1}{2} \\times a \\times c \\times sin\\;(B)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of an equilateral triangle $= \\frac{1}{2} \\times a \\times a \\times sin\\;(C)$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{1}{2} \\times a^2 \\times sin\\;(60^\\circ)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{1}{2}\\times a^2 \\times \\frac{\\sqrt{3}}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Area of an equilateral triangle <\/strong>$= \\frac{\\sqrt{3}a^2}{4}$<strong> square units<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-properties-of-equilateral-triangle\">Properties of Equilateral Triangle<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">All sides are equal in length.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">All angles are congruent. Each angle measures $60^\\circ$. Thus, it is equiangular.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">It is a regular polygon.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The area of an equilateral triangle is $\\frac{\\sqrt{3}a^2}{4}$<strong>.<\/strong><\/li>\n\n\n\n<li class=\"eplus-wrapper\">The perimeter of an equilateral triangle is 3a.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">In an equilateral triangle, the median, angle bisector, and perpendicular are all the same.&nbsp;<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-facts-about-area-of-equilateral-triangle\">Facts about Area of Equilateral Triangle<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">You can simplify the Heron\u2019s formula for the equilateral triangle as:<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of an equilateral triangle $=&nbsp;\\sqrt{s(s\\;-\\;a)^3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">where $s = \\frac{3a}{2}$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Area of an equilateral triangle can also be calculated if the perimeter is known.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of an equilateral triangle is 3a.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Find the side using this formula and substitute in the formula: Area $= \\frac{\\sqrt{3}a^2}{4}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-solved-examples-on-area-of-equilateral-triangle\">Solved Examples on Area of Equilateral Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Find the area of an equilateral triangle whose perimeter is 12 inches.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let the side of an equilateral triangle be a inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter $= 12$ in<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of an equilateral triangle $= 3a$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow 3a = 12$ in<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow a = 4$ in<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area = \\frac{\\sqrt{3}a^2}{4} = \\frac{\\sqrt{3}(4)^2}{4} = \\frac{16\\sqrt{3}}{4} = 4\\sqrt{3}\\; in^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. If the area of an equilateral triangle is <\/strong>$16\\sqrt{3}\\; ft^2$<strong>, find the side of the triangle.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area = 16\\sqrt{3}\\; ft^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let the side of an equilateral triangle be a ft.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{\\sqrt{3}a^2}{4} = 16\\sqrt{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow a^2 = 64$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow a = 8\\; ft$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Side of the triangle $= 8\\; ft$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Find the area of an equilateral triangle whose height is <\/strong>$5\\sqrt{3}$<strong> units.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Height $= h = \\frac{\\sqrt{3}a}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$5\\sqrt{3} = \\frac{\\sqrt{3}a}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a = 10$ unit<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area = \\frac{\\sqrt{3a^2}}{4} = \\frac{\\sqrt{3}(10)^2}{4} = \\frac{100\\sqrt{3}}{4} = 25\\sqrt{3}$ square units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. If the side of an equilateral triangle doubles, then by how much the area will increase?<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let the side of an equilateral triangle be a units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Original Area $= \\frac{\\sqrt{3}a^2}{4}$ square units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">New side $= 2a$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">New Area $= \\frac{3(2a)^2}{4} = \\sqrt{3}a^2$ square units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Increase in area $= \\sqrt{3}a^2\\;\u2013\\;\\frac{\\sqrt{3}a^2}{4} = \\frac{3\\sqrt{3}a^2}{4}$ square units<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-practice-problems-on-area-of-equilateral-triangle\">Practice Problems on Area of Equilateral Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Area of an Equilateral Triangle - Formula, Derivation, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Find the area of an equilateral triangle whose side is 14 ft.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$196\\;ft^2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$108\\;ft^2$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$123\\;ft^2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$493\\;ft^2$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $493\\;ft^2$<br\/>Side $= 14\\;ft$<br>\r\n$Area = \\frac{\\sqrt{3}a^2}{4} = \\frac{\\sqrt{3}\\times14\\times14}{4} = 49\\sqrt{3}\\;ft^2$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Find the area of an equilateral triangle whose height is $12\\sqrt{3}$ inches.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$243\\;in^2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$1443\\;in^2$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$1243\\;in^2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$2043\\;in^2$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $1443\\;in^2$<br\/>Height $= h = \\frac{\\sqrt{3}a}{2}$<br>\r\n$12\\sqrt{3} = \\frac{\\sqrt{3}a}{2}$<br>\r\n$a = 24$ inches<br>\r\nArea $= \\frac{\\sqrt{3}a^2}{4} = \\frac{\\sqrt{3}(24)^2}{4} = \\frac{5763}{4} = 144\\sqrt{3}\\;in^2$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Find the area of an equilateral triangle whose perimeter is $6\\sqrt{2}\\;ft$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$24\\;ft^2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$3\\sqrt{2}\\;ft^2$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$2\\sqrt{3}\\;ft^2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$72\\;ft^2$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $2\\sqrt{3}\\;ft^2$<br\/>Perimeter $= 6\\sqrt{2}$ feet<br>\r\n $3a = 6\\sqrt{2}$ feet<br>\r\n$\\Rightarrow  a = 2\\sqrt{2}$ feet<br>\r\nArea $= \\frac{\\sqrt{3}a^2}{4} = \\frac{\\sqrt{3}(2\\sqrt{2})^2}{4} = \\frac{8\\sqrt{3}}{4} = 2\\sqrt{3}\\;ft^2$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">If the side of an equilateral triangle triples, then the ratio of new area to old area is _______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1 : 9<\/div><div class=\"spq_answer_block\" data-value=\"1\">9 : 1<\/div><div class=\"spq_answer_block\" data-value=\"2\">2 : 3<\/div><div class=\"spq_answer_block\" data-value=\"3\">1 : 4<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 9 : 1<br\/>Let original side be a units.<br>\r\nOriginal Area $= \\frac{\\sqrt{3}a^2}{4}$ square units<br>\r\n$New side = 3a$ units<br>\r\n$New Area = \\frac{\\sqrt{3}(3a)^2}{4} = \\frac{9\\sqrt{3}a^2}{4}$ square units<br>\r\n$Ratio = \\frac{93a2}{4}\\;:\\;\\frac{\\sqrt{3}a^2}{4} = 9 :1$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Find the perimeter of an equilateral triangle whose area is $8\\sqrt{3}\\;ft^2$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$12\\sqrt{2}\\;ft$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$12\\;ft$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$24\\sqrt{2}\\;ft$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$24\\;ft$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $12\\sqrt{2}\\;ft$<br\/>$8\\sqrt{3} = \\frac{\\sqrt{3}a2}{4}$<br>\r\n$32 = a^2$<br>\r\n$a = 4\\sqrt{2}\\;ft$<br>\r\n$Perimeter = 3a = 3\\times4\\sqrt{2}=12\\sqrt{2}\\;ft$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Area of an Equilateral Triangle - Formula, Derivation, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Area of an Equilateral Triangle\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the area of an equilateral triangle whose side is 14 ft.\",\n                    \"text\": \"Find the area of an equilateral triangle whose side is 14 ft.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Side $$= 14\\\\;ft$$<br>\r\n$$Area = \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}\\\\times14\\\\times14}{4} = 49\\\\sqrt{3}\\\\;ft^2$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$196\\\\;ft^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Side $$= 14\\\\;ft$$<br>\r\n$$Area = \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}\\\\times14\\\\times14}{4} = 49\\\\sqrt{3}\\\\;ft^2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$108\\\\;ft^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Side $$= 14\\\\;ft$$<br>\r\n$$Area = \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}\\\\times14\\\\times14}{4} = 49\\\\sqrt{3}\\\\;ft^2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$123\\\\;ft^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Side $$= 14\\\\;ft$$<br>\r\n$$Area = \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}\\\\times14\\\\times14}{4} = 49\\\\sqrt{3}\\\\;ft^2$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$493\\\\;ft^2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Side $$= 14\\\\;ft$$<br>\r\n$$Area = \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}\\\\times14\\\\times14}{4} = 49\\\\sqrt{3}\\\\;ft^2$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Side $$= 14\\\\;ft$$<br>\r\n$$Area = \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}\\\\times14\\\\times14}{4} = 49\\\\sqrt{3}\\\\;ft^2$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the area of an equilateral triangle whose height is $$12\\\\sqrt{3}$$ inches.\",\n                    \"text\": \"Find the area of an equilateral triangle whose height is $$12\\\\sqrt{3}$$ inches.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Height $$= h = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$12\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$a = 24$$ inches<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(24)^2}{4} = \\\\frac{5763}{4} = 144\\\\sqrt{3}\\\\;in^2$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$243\\\\;in^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Height $$= h = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$12\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$a = 24$$ inches<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(24)^2}{4} = \\\\frac{5763}{4} = 144\\\\sqrt{3}\\\\;in^2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$1243\\\\;in^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Height $$= h = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$12\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$a = 24$$ inches<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(24)^2}{4} = \\\\frac{5763}{4} = 144\\\\sqrt{3}\\\\;in^2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2043\\\\;in^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Height $$= h = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$12\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$a = 24$$ inches<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(24)^2}{4} = \\\\frac{5763}{4} = 144\\\\sqrt{3}\\\\;in^2$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$1443\\\\;in^2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Height $$= h = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$12\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$a = 24$$ inches<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(24)^2}{4} = \\\\frac{5763}{4} = 144\\\\sqrt{3}\\\\;in^2$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Height $$= h = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$12\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a}{2}$$<br>\r\n$$a = 24$$ inches<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(24)^2}{4} = \\\\frac{5763}{4} = 144\\\\sqrt{3}\\\\;in^2$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the area of an equilateral triangle whose perimeter is $$6\\\\sqrt{2}\\\\;ft$$.\",\n                    \"text\": \"Find the area of an equilateral triangle whose perimeter is $$6\\\\sqrt{2}\\\\;ft$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Perimeter $$= 6\\\\sqrt{2}$$ feet<br>\r\n $$3a = 6\\\\sqrt{2}$$ feet<br>\r\n$$\\\\Rightarrow  a = 2\\\\sqrt{2}$$ feet<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(2\\\\sqrt{2})^2}{4} = \\\\frac{8\\\\sqrt{3}}{4} = 2\\\\sqrt{3}\\\\;ft^2$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$24\\\\;ft^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter $$= 6\\\\sqrt{2}$$ feet<br>\r\n $$3a = 6\\\\sqrt{2}$$ feet<br>\r\n$$\\\\Rightarrow  a = 2\\\\sqrt{2}$$ feet<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(2\\\\sqrt{2})^2}{4} = \\\\frac{8\\\\sqrt{3}}{4} = 2\\\\sqrt{3}\\\\;ft^2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$3\\\\sqrt{2}\\\\;ft^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter $$= 6\\\\sqrt{2}$$ feet<br>\r\n $$3a = 6\\\\sqrt{2}$$ feet<br>\r\n$$\\\\Rightarrow  a = 2\\\\sqrt{2}$$ feet<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(2\\\\sqrt{2})^2}{4} = \\\\frac{8\\\\sqrt{3}}{4} = 2\\\\sqrt{3}\\\\;ft^2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$72\\\\;ft^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter $$= 6\\\\sqrt{2}$$ feet<br>\r\n $$3a = 6\\\\sqrt{2}$$ feet<br>\r\n$$\\\\Rightarrow  a = 2\\\\sqrt{2}$$ feet<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(2\\\\sqrt{2})^2}{4} = \\\\frac{8\\\\sqrt{3}}{4} = 2\\\\sqrt{3}\\\\;ft^2$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$2\\\\sqrt{3}\\\\;ft^2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Perimeter $$= 6\\\\sqrt{2}$$ feet<br>\r\n $$3a = 6\\\\sqrt{2}$$ feet<br>\r\n$$\\\\Rightarrow  a = 2\\\\sqrt{2}$$ feet<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(2\\\\sqrt{2})^2}{4} = \\\\frac{8\\\\sqrt{3}}{4} = 2\\\\sqrt{3}\\\\;ft^2$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Perimeter $$= 6\\\\sqrt{2}$$ feet<br>\r\n $$3a = 6\\\\sqrt{2}$$ feet<br>\r\n$$\\\\Rightarrow  a = 2\\\\sqrt{2}$$ feet<br>\r\nArea $$= \\\\frac{\\\\sqrt{3}a^2}{4} = \\\\frac{\\\\sqrt{3}(2\\\\sqrt{2})^2}{4} = \\\\frac{8\\\\sqrt{3}}{4} = 2\\\\sqrt{3}\\\\;ft^2$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the side of an equilateral triangle triples, then the ratio of new area to old area is _______.\",\n                    \"text\": \"If the side of an equilateral triangle triples, then the ratio of new area to old area is _______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Let original side be a units.<br>\r\nOriginal Area $$= \\\\frac{\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$New side = 3a$$ units<br>\r\n$$New Area = \\\\frac{\\\\sqrt{3}(3a)^2}{4} = \\\\frac{9\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$Ratio = \\\\frac{93a2}{4}\\\\;:\\\\;\\\\frac{\\\\sqrt{3}a^2}{4} = 9 :1$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1 : 9\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let original side be a units.<br>\r\nOriginal Area $$= \\\\frac{\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$New side = 3a$$ units<br>\r\n$$New Area = \\\\frac{\\\\sqrt{3}(3a)^2}{4} = \\\\frac{9\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$Ratio = \\\\frac{93a2}{4}\\\\;:\\\\;\\\\frac{\\\\sqrt{3}a^2}{4} = 9 :1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2 : 3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let original side be a units.<br>\r\nOriginal Area $$= \\\\frac{\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$New side = 3a$$ units<br>\r\n$$New Area = \\\\frac{\\\\sqrt{3}(3a)^2}{4} = \\\\frac{9\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$Ratio = \\\\frac{93a2}{4}\\\\;:\\\\;\\\\frac{\\\\sqrt{3}a^2}{4} = 9 :1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1 : 4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let original side be a units.<br>\r\nOriginal Area $$= \\\\frac{\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$New side = 3a$$ units<br>\r\n$$New Area = \\\\frac{\\\\sqrt{3}(3a)^2}{4} = \\\\frac{9\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$Ratio = \\\\frac{93a2}{4}\\\\;:\\\\;\\\\frac{\\\\sqrt{3}a^2}{4} = 9 :1$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"9 : 1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let original side be a units.<br>\r\nOriginal Area $$= \\\\frac{\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$New side = 3a$$ units<br>\r\n$$New Area = \\\\frac{\\\\sqrt{3}(3a)^2}{4} = \\\\frac{9\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$Ratio = \\\\frac{93a2}{4}\\\\;:\\\\;\\\\frac{\\\\sqrt{3}a^2}{4} = 9 :1$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let original side be a units.<br>\r\nOriginal Area $$= \\\\frac{\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$New side = 3a$$ units<br>\r\n$$New Area = \\\\frac{\\\\sqrt{3}(3a)^2}{4} = \\\\frac{9\\\\sqrt{3}a^2}{4}$$ square units<br>\r\n$$Ratio = \\\\frac{93a2}{4}\\\\;:\\\\;\\\\frac{\\\\sqrt{3}a^2}{4} = 9 :1$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the perimeter of an equilateral triangle whose area is $$8\\\\sqrt{3}\\\\;ft^2$$.\",\n                    \"text\": \"Find the perimeter of an equilateral triangle whose area is $$8\\\\sqrt{3}\\\\;ft^2$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$8\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a2}{4}$$<br>\r\n$$32 = a^2$$<br>\r\n$$a = 4\\\\sqrt{2}\\\\;ft$$<br>\r\n$$Perimeter = 3a = 3\\\\times4\\\\sqrt{2}=12\\\\sqrt{2}\\\\;ft$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$12\\\\;ft$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$8\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a2}{4}$$<br>\r\n$$32 = a^2$$<br>\r\n$$a = 4\\\\sqrt{2}\\\\;ft$$<br>\r\n$$Perimeter = 3a = 3\\\\times4\\\\sqrt{2}=12\\\\sqrt{2}\\\\;ft$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$24\\\\sqrt{2}\\\\;ft$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$8\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a2}{4}$$<br>\r\n$$32 = a^2$$<br>\r\n$$a = 4\\\\sqrt{2}\\\\;ft$$<br>\r\n$$Perimeter = 3a = 3\\\\times4\\\\sqrt{2}=12\\\\sqrt{2}\\\\;ft$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$24\\\\;ft$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$8\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a2}{4}$$<br>\r\n$$32 = a^2$$<br>\r\n$$a = 4\\\\sqrt{2}\\\\;ft$$<br>\r\n$$Perimeter = 3a = 3\\\\times4\\\\sqrt{2}=12\\\\sqrt{2}\\\\;ft$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$12\\\\sqrt{2}\\\\;ft$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$8\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a2}{4}$$<br>\r\n$$32 = a^2$$<br>\r\n$$a = 4\\\\sqrt{2}\\\\;ft$$<br>\r\n$$Perimeter = 3a = 3\\\\times4\\\\sqrt{2}=12\\\\sqrt{2}\\\\;ft$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$8\\\\sqrt{3} = \\\\frac{\\\\sqrt{3}a2}{4}$$<br>\r\n$$32 = a^2$$<br>\r\n$$a = 4\\\\sqrt{2}\\\\;ft$$<br>\r\n$$Perimeter = 3a = 3\\\\times4\\\\sqrt{2}=12\\\\sqrt{2}\\\\;ft$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-frequently-asked-questions-on-area-of-equilateral-triangles\">Frequently Asked Questions on Area of Equilateral Triangles<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-12b7603c-4f9e-4779-b180-be8dade84773\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-12b7603c-4f9e-4779-b180-be8dade84773\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-12b7603c-4f9e-4779-b180-be8dade84773\"><strong>What is the difference between the area and perimeter of an equilateral triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-12b7603c-4f9e-4779-b180-be8dade84773\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The area of an equilateral triangle is the region enclosed within the boundary of the triangle. We can calculate the area of triangle using the formula $\\frac{\\sqrt{3}a^2}{4}$ , where a is the side of the triangle. It is measured in square units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The perimeter of an equilateral triangle is the length of the outline of the equilateral triangle. We can calculate the perimeter of equilateral triangle by using the formula 3a where a is the side of the triangle.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-12b7603c-4f9e-4779-b180-be8dade84773\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-12b7603c-4f9e-4779-b180-be8dade84773\"><strong>What is the relation between area and perimeter of an equilateral triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-12b7603c-4f9e-4779-b180-be8dade84773\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of an equilateral triangle $= 3a$, where $a$ is the side of the triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $a = \\frac{Perimeter}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area = \\frac{\\sqrt{3}a^2}{4} = \\frac{\\sqrt{3}}{4}\\times\\frac{Perimeter}{3}\\times\\frac{Perimeter}{3} = \\frac{(Perimeter)^2}{12\\sqrt{3}}$ square units<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-12b7603c-4f9e-4779-b180-be8dade84773\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-12b7603c-4f9e-4779-b180-be8dade84773\"><strong>What are the formulas for the area of an equilateral triangle in terms of its altitude, median, and angle bisectors?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-12b7603c-4f9e-4779-b180-be8dade84773\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let a be the side of the triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Altitude = Median = Angle \\;Bisector = h = \\frac{\\sqrt{3}a}{2}\\Rightarrow a = \\frac{2h}{\\sqrt{3}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area = \\frac{\\sqrt{3}}{4}\\times(\\frac{2h}{\\sqrt{3}})^2 = \\frac{h^2}{\\sqrt{3}}$ square units<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-12b7603c-4f9e-4779-b180-be8dade84773\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-12b7603c-4f9e-4779-b180-be8dade84773\"><strong>What are the formulas for perimeter of an equilateral triangle in terms of its altitude, median and angle bisectors?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-12b7603c-4f9e-4779-b180-be8dade84773\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let $a$ be the side of the triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Altitude = Median = Angle\\;Bisector = h = \\frac{\\sqrt{3}a}{2}\\Rightarrow a = \\frac{2h}{\\sqrt{3}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Perimeter = 3a = 3\\times\\frac{2h}{\\sqrt{3}} = 2h\\sqrt{3}$ units<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-12b7603c-4f9e-4779-b180-be8dade84773\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-12b7603c-4f9e-4779-b180-be8dade84773\"><strong>What is the difference between an equilateral and an isosceles triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-12b7603c-4f9e-4779-b180-be8dade84773\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An equilateral triangle is a triangle whose all sides are of equal measure and all angles are equal and are of $60^\\circ$ each, whereas an isosceles triangle is a triangle whose two sides are of equal measure.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Area of an Equilateral Triangle? Area of an equilateral is the region bounded within the three sides of the triangle. In other words, the area of an equilateral triangle is the total region enclosed within the boundary of the triangle. It is calculated using the simple formula $\\frac{\\sqrt{3}}{4} \\times a^2$, where \u201ca\u201d &#8230; <a title=\"Area of an Equilateral Triangle &#8211; Formula, Derivation, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-equilateral-triangle\" aria-label=\"More on Area of an Equilateral Triangle &#8211; Formula, Derivation, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-27503","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27503","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=27503"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27503\/revisions"}],"predecessor-version":[{"id":39913,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27503\/revisions\/39913"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=27503"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=27503"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=27503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}