{"id":25883,"date":"2023-03-06T06:23:05","date_gmt":"2023-03-06T06:23:05","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=25883"},"modified":"2024-02-05T15:35:30","modified_gmt":"2024-02-05T15:35:30","slug":"height-of-equilateral-triangle","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/height-of-equilateral-triangle","title":{"rendered":"Height of Equilateral Triangle &#8211; Formula, Method, 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-2bb1de38-650c-488b-9698-fe286157f01c\" 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\/height-of-equilateral-triangle#0-what-is-the-height-of-an-equilateral-triangle>What is the Height of an Equilateral Triangle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/height-of-equilateral-triangle#4-height-of-equilateral-triangle-formula-proof>Height of Equilateral Triangle Formula Proof<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/height-of-equilateral-triangle#5-how-to-find-the-height-of-an-equilateral-triangle-when-the-side-is-given->How to Find the Height of an Equilateral Triangle When the Side is Given?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/height-of-equilateral-triangle#9-solved-examples-on-height-of-equilateral-triangle>Solved Examples On Height of Equilateral Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/height-of-equilateral-triangle#10-practice-problems-on-height-of-equilateral-triangle>Practice Problems On Height of Equilateral Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/height-of-equilateral-triangle#11-frequently-asked-questions-on-height-of-equilateral-triangle>Frequently Asked Questions On Height of Equilateral Triangle<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-height-of-an-equilateral-triangle\">What is the Height of an Equilateral Triangle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Height is a term that we use to describe how tall an object is when measured vertically. <strong>Height of an equilateral triangle is described as the length of the equilateral triangle measured from its top vertex to the base<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-height-of-equilateral-triangle-definition-\">Height of Equilateral Triangle: Definition&nbsp;<\/h3>\n\n\n\n<p class=\"eplus-wrapper\"><strong>An equilateral triangle has all of its three sides equal in length<\/strong>. In this triangle, one will draw a straight line from one of the vertices to the opposite side of the triangle, and that line divides the equilateral triangle into two parts of equal area, which is termed as the height of an equilateral triangle, please have a look at the attached image where line AO is the height of an equilateral triangle ABC.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"430\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/height-of-an-equilateral-triangle.webp\" alt=\"Height of an equilateral triangle\" class=\"wp-image-33148\" title=\"Height of an equilateral triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/height-of-an-equilateral-triangle.webp 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/height-of-an-equilateral-triangle-300x208.webp 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\/align-and-compare-heights\" 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\/measurement_heights_align_compare_pt.png\" alt=\"Align and Compare Heights 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\">Align and Compare Heights 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\/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\/compare-heights-of-objects\" 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\/measurement_heights_equal_not_pt.png\" alt=\"Compare Heights of Objects 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\">Compare Heights of Objects 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\/identify-the-object-with-shorter-height\" 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\/measurement_which_height_shorter_pt.png\" alt=\"Identify the Object with Shorter Height 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\">Identify the Object with Shorter Height 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\/identify-the-type-of-triangles-based-on-angles\" 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_angle_pt.png\" alt=\"Identify the Type of Triangles Based on Angles 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\">Identify the Type of Triangles Based on Angles 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\/identify-triangles-and-rectangles\" 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_amusement_park_18_20_gm.png\" alt=\"Identify Triangles and Rectangles 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\">Identify Triangles and Rectangles 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\/identify-triangles-and-squares\" 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_triangles_squares_pt.png\" alt=\"Identify Triangles and Squares 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\">Identify Triangles and Squares 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\/identify-types-of-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_types_of_triangles_pt.png\" alt=\"Identify Types of 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\">Identify Types of 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><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 = slidesContainer.querySelectorAll(\".game-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-what-are-the-important-characteristics-of-height-of-equilateral-triangle\">What Are the Important Characteristics of Height of Equilateral Triangle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In the above equilateral triangle ABC, we have defined that AO is the height of the triangle.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The right-angled triangles formed are $\\angle AOB$ and $\\angle AOC$. The areas of the two right-angled triangles AOB and AOC formed by AO are equal.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Interestingly, this line AO, divides $\\angle BAC$ into two equal parts, such that,$\\angle BAC = \\frac{\\angle BAO}{2} + \\frac{\\angle CAO}{2}$ And therefore this line AO is also called as angle bisector of the $\\angle BAC$ alongwith the height of an equilateral triangle.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Further, the line AO divides the opposite side BC into two equal parts of BO and OC, and makes an angle of $90^{\\circ}$ with the base BC. So, it is a perpendicular bisector of the line segment BC.&nbsp;<\/li>\n<\/ul>\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\/compare-heights\" 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-heights.jpeg\" alt=\"Compare Heights 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\/comparing-heights-of-objects\" 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\/comparing-heights-of-objects.jpeg\" alt=\"Comparing Heights of Objects 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\/order-heights-of-given-plants\" 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\/order-heights-of-given-plants.jpeg\" alt=\"Order Heights of Given Plants\">\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\/rank-kids-in-ascending-order-of-their-heights\" 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\/rank-kids-in-ascending-order-of-their-heights.jpeg\" alt=\"Rank Kids in Ascending Order of Their Heights\">\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\/rectangles-and-triangles\" 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\/rectangles-and-triangles.jpeg\" alt=\"Rectangles and Triangles 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\/separate-out-the-triangles\" 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\/separate-out-the-triangles.jpeg\" alt=\"Separate Out the Triangles 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><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More 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=\"3-height-of-equilateral-triangle-formula\">Height of Equilateral Triangle Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The formula for the height of an equilateral triangle (h) is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = \\frac{\\sqrt{3}}{2}a$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, a represents the side of the equilateral triangle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-height-of-equilateral-triangle-formula-proof\">Height of Equilateral Triangle Formula Proof<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">To calculate the height of an equilateral triangle, we will apply the Pythagorean theorem in the right-angled triangle AOC, given below. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of adjacent and perpendicular. Therefore, in triangle AOC, we can write,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(AC)^{2} = (AO)^{2} + (OC)^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(a)^{2} = (h)^{2} + \\bigg(\\frac{a}{2} \\bigg)^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(h)^{2} = (a)^{2} \\;-\\; \\bigg(\\frac{a}{2} \\bigg)^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h^{2} = a^{2}\\;-\\;\\frac{1}{4}a^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h^{2} = \\frac{3}{4}a^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = \\sqrt{\\frac{3}{4}a}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = \\frac{\\sqrt{3}}{2}a$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the height of an equilateral triangle formula, h, is $\\frac{\\sqrt{3}}{2}$ times of the side of the equilateral triangle, a.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"400\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/height-of-an-equilateral-triangle-formula.png\" alt=\"Height of an equilateral triangle formula\" class=\"wp-image-33150\" title=\"Height of an equilateral triangle formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/height-of-an-equilateral-triangle-formula.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/height-of-an-equilateral-triangle-formula-300x194.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-how-to-find-the-height-of-an-equilateral-triangle-when-the-side-is-given-\">How to Find the Height of an Equilateral Triangle When the Side is Given?<br><\/h2>\n\n\n\n<p class=\"eplus-wrapper\">If the side of an equilateral triangle is given, then we can simply use the formula to find the height.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = \\frac{\\sqrt{3}}{2}a$ \u2026where \u2018a\u2019 is the side<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-how-to-find-the-height-of-an-equilateral-triangle-when-the-perimeter-of-the-triangle-is-given\">How to Find the Height of an Equilateral Triangle When the Perimeter of the Triangle Is Given?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The perimeter of an object is defined as the measure of the length of the shape. Therefore, for an equilateral triangle the perimeter can be given as the sum of all its three sides, which can be given as,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Perimeter $= a + a + a = 3a$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, once we know the value of perimeter, we can determine the side of an equilateral triangle by using the formula,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a = \\frac{Perimeter}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, finding the height of an equilateral triangle is easy. We use the formula $h = \\frac{\\sqrt{3}}{2}a$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = \\frac{\\sqrt{3}}{2}a = \\frac{\\sqrt{3}}{2} \\times \\frac{Perimeter}{3} = \\frac{Perimeter}{2\\sqrt{3}}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-how-to-calculate-the-height-of-an-equilateral-triangle-when-the-area-of-the-triangle-is-given\">How to Calculate the Height of an Equilateral Triangle When the Area of the Triangle Is Given?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The area of an equilateral triangle is define with the formula<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area $= \\frac{\\sqrt{3}}{4}(a)^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, if we know the value of area of an equilateral triangle then, using the above equation we can determine the value of a, which can be used to estimate the height of an equilateral triangle using the formula,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = \\frac{\\sqrt{3}}{2}a$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned that the height of an equilateral triangle is defined as the distance from the vertex of the triangle and opposite side of this vertex, and this can be calculated mathematically using the derived formulas in the article. All the heights of an equilateral triangle are equal since the sides of the equilateral triangle are equal.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-solved-examples-on-height-of-equilateral-triangle\">Solved Examples On Height of Equilateral Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Find the height of an equilateral triangle if its side is 5 units.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given, side of the equilateral triangle $= a = 5$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We have to find the height of the equilateral triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Use the formula to calculate the height of an equilateral triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = \\frac{\\sqrt{3}}{2}a = \\frac{\\sqrt{3}}{2} \\times 5\\; units = 4.33$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus the height of an equilateral triangle is 4.33 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Find the height of an equilateral triangle if its perimeter is 12<\/strong>3<strong> units.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Perimeter of the equilateral triangle $= 3a = 12\\sqrt{3}$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We have to find the height of the equilateral triangle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = ?$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, we can use the formula to calculate the height of an equilateral triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = \\frac{Perimeter}{2\\sqrt{3}} = \\frac{12\\sqrt{3}}{2\\sqrt{3}}\\; units = 6\\; units$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the height of an equilateral triangle is 3.46 units, which has a perimeter of 12 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Find the height of an equilateral triangle if its Area is <\/strong>$4\\sqrt{3}$<strong> square units.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> Area of the equilateral triangle $= \\frac{\\sqrt{3}}{4}(a)^{2} = 4\\sqrt{3}$ square units<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We have to find the height of the equilateral triangle $h = ?$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, first we can use the formula to calculate the side of an equilateral triangle, such that,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{\\sqrt{3}}{4}(a)^{2} = 4\\sqrt{3}\\; square\\; units$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a^{2} = \\frac{4}{\\sqrt{3}} \\times 4\\sqrt{3}\\; square\\; units$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a^{2} = 16\\; square\\; units$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a = 4\\; units$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, we can use this value to calculate the height of an equilateral triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = \\frac{\\sqrt{3}}{2}a = \\frac{\\sqrt{3}}{2} \\times 4\\; units = 2\\sqrt{3}\\; units$<br>Thus, the height of an equilateral triangle is $2\\sqrt{3}\\;$ units.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-practice-problems-on-height-of-equilateral-triangle\">Practice Problems On Height of Equilateral Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Height of Equilateral Triangle<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Find the height of an equilateral triangle if its side is $4\\sqrt{3}$ units.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5 units<\/div><div class=\"spq_answer_block\" data-value=\"1\">12 units<\/div><div class=\"spq_answer_block\" data-value=\"2\">6 units<\/div><div class=\"spq_answer_block\" data-value=\"3\">9 units<\/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: 6 units<br\/>We will use the formula $h = \\frac{\\sqrt{3}}{2}a$ to estimate the height of an equilateral triangle.<br>\r\n$h = \\frac{\\sqrt{3}}{2} \\times 4\\sqrt{3} = 6\\; units$<\/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 height of an equilateral triangle if its side is 8 units.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">8.57 units<\/div><div class=\"spq_answer_block\" data-value=\"1\">6.93 units<\/div><div class=\"spq_answer_block\" data-value=\"2\">6.15 units<\/div><div class=\"spq_answer_block\" data-value=\"3\">9.27 units<\/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: 6.93 units<br\/>We will use the formula $h = \\frac{\\sqrt{3}}{2}a$ to estimate the height of an equilateral triangle.<br>\r\n$h = \\frac{\\sqrt{3}}{2} \\times 8 = 4\\sqrt{3} \\approx 6.93\\; units$<\/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 height of an equilateral triangle if its area is 50 square units.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">14.7 units<\/div><div class=\"spq_answer_block\" data-value=\"1\">15.5 units<\/div><div class=\"spq_answer_block\" data-value=\"2\">9.3 units<\/div><div class=\"spq_answer_block\" data-value=\"3\">12.2 units<\/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: 9.3 units<br\/>We will first calculate the side of the equilateral triangle using the formula for area, i.e., $\\frac{\\sqrt{3}}{4}a^{2}$, <br>\r\n$a = \\frac{\\sqrt{4\\times Area}}{\\sqrt{3}}\\approx 10.74$ and then using the formula for height $h = \\frac{\\sqrt{3}}{2}\\times 10.74\\approx 9.3$ units, calculate the height.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Find the height of an equilateral triangle if its perimeter is 27 units.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">7.8 units<\/div><div class=\"spq_answer_block\" data-value=\"1\">8 units<\/div><div class=\"spq_answer_block\" data-value=\"2\">9 units<\/div><div class=\"spq_answer_block\" data-value=\"3\">10 units<\/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: 7.8 units<br\/>$h = \\frac{Perimeter}{2\\sqrt{3}} = \\frac{27}{2\\sqrt{3}}\\approx 7.8\\; units$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Find the height of an equilateral triangle if its area is 100 square units.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">20.24 units<\/div><div class=\"spq_answer_block\" data-value=\"1\">13.16 units<\/div><div class=\"spq_answer_block\" data-value=\"2\">26.37 units<\/div><div class=\"spq_answer_block\" data-value=\"3\">30.71 units<\/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: 13.16 units<br\/>We will first calculate the side of the equilateral triangle using the formula for calculating the area.<br>\r\nArea $=100=\\frac{\\sqrt{3}}{4}$a$^{2}$<br>\r\n$a=\\sqrt{\\frac{4 \\times Area}{ \\sqrt{3}}} \\approx 15.19$ square units<br>\r\nNow use the formula for height.<br>\r\n$h=\\frac{\\sqrt{3}}{2}\\times15.19\\approx13.16$ units<\/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     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1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will use the formula $$h = \\\\frac{\\\\sqrt{3}}{2}a$$ to estimate the height of an equilateral triangle.<br>\r\n$$h = \\\\frac{\\\\sqrt{3}}{2} \\\\times 4\\\\sqrt{3} = 6\\\\; units$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"9 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will use the formula $$h = \\\\frac{\\\\sqrt{3}}{2}a$$ to estimate the height of an equilateral triangle.<br>\r\n$$h = \\\\frac{\\\\sqrt{3}}{2} \\\\times 4\\\\sqrt{3} = 6\\\\; units$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"6 units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We will use the formula $$h = \\\\frac{\\\\sqrt{3}}{2}a$$ to estimate the height of an equilateral triangle.<br>\r\n$$h = \\\\frac{\\\\sqrt{3}}{2} \\\\times 4\\\\sqrt{3} = 6\\\\; units$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We will use the formula $$h = \\\\frac{\\\\sqrt{3}}{2}a$$ to estimate the height of an equilateral triangle.<br>\r\n$$h = \\\\frac{\\\\sqrt{3}}{2} \\\\times 4\\\\sqrt{3} = 6\\\\; units$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the height of an equilateral triangle if its side is 8 units.\",\n                    \"text\": \"Find the height of an equilateral triangle if its side is 8 units.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We will use the formula $$h = \\\\frac{\\\\sqrt{3}}{2}a$$ to estimate the height of an equilateral triangle.<br>\r\n$$h = \\\\frac{\\\\sqrt{3}}{2} \\\\times 8 = 4\\\\sqrt{3} \\\\approx 6.93\\\\; units$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8.57 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will use the formula $$h = \\\\frac{\\\\sqrt{3}}{2}a$$ to estimate the height of an equilateral triangle.<br>\r\n$$h = \\\\frac{\\\\sqrt{3}}{2} \\\\times 8 = 4\\\\sqrt{3} \\\\approx 6.93\\\\; units$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6.15 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will use the formula $$h = \\\\frac{\\\\sqrt{3}}{2}a$$ to estimate the height of an equilateral triangle.<br>\r\n$$h = \\\\frac{\\\\sqrt{3}}{2} \\\\times 8 = 4\\\\sqrt{3} \\\\approx 6.93\\\\; units$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"9.27 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will use the formula $$h = \\\\frac{\\\\sqrt{3}}{2}a$$ to estimate the height of an equilateral triangle.<br>\r\n$$h = \\\\frac{\\\\sqrt{3}}{2} \\\\times 8 = 4\\\\sqrt{3} \\\\approx 6.93\\\\; units$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"6.93 units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We will use the formula $$h = \\\\frac{\\\\sqrt{3}}{2}a$$ to estimate the height of an equilateral triangle.<br>\r\n$$h = \\\\frac{\\\\sqrt{3}}{2} \\\\times 8 = 4\\\\sqrt{3} \\\\approx 6.93\\\\; units$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We will use the formula $$h = \\\\frac{\\\\sqrt{3}}{2}a$$ to estimate the height of an equilateral triangle.<br>\r\n$$h = \\\\frac{\\\\sqrt{3}}{2} \\\\times 8 = 4\\\\sqrt{3} \\\\approx 6.93\\\\; units$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the height of an equilateral triangle if its area is 50 square units.\",\n                    \"text\": \"Find the height of an equilateral triangle if its area is 50 square units.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We will first calculate the side of the equilateral triangle using the formula for area, i.e., $$\\\\frac{\\\\sqrt{3}}{4}a^{2}$$, <br>\r\n$$a = \\\\frac{\\\\sqrt{4\\\\times Area}}{\\\\sqrt{3}}\\\\approx 10.74$$ and then using the formula for height $$h = \\\\frac{\\\\sqrt{3}}{2}\\\\times 10.74\\\\approx 9.3$$ units, calculate the height.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"14.7 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will first calculate the side of the equilateral triangle using the formula for area, i.e., $$\\\\frac{\\\\sqrt{3}}{4}a^{2}$$, <br>\r\n$$a = \\\\frac{\\\\sqrt{4\\\\times Area}}{\\\\sqrt{3}}\\\\approx 10.74$$ and then using the formula for height $$h = \\\\frac{\\\\sqrt{3}}{2}\\\\times 10.74\\\\approx 9.3$$ units, calculate the height.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"15.5 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will first calculate the side of the equilateral triangle using the formula for area, i.e., $$\\\\frac{\\\\sqrt{3}}{4}a^{2}$$, <br>\r\n$$a = \\\\frac{\\\\sqrt{4\\\\times Area}}{\\\\sqrt{3}}\\\\approx 10.74$$ and then using the formula for height $$h = \\\\frac{\\\\sqrt{3}}{2}\\\\times 10.74\\\\approx 9.3$$ units, calculate the height.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12.2 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will first calculate the side of the equilateral triangle using the formula for area, i.e., $$\\\\frac{\\\\sqrt{3}}{4}a^{2}$$, <br>\r\n$$a = \\\\frac{\\\\sqrt{4\\\\times Area}}{\\\\sqrt{3}}\\\\approx 10.74$$ and then using the formula for height $$h = \\\\frac{\\\\sqrt{3}}{2}\\\\times 10.74\\\\approx 9.3$$ units, calculate the height.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"9.3 units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We will first calculate the side of the equilateral triangle using the formula for area, i.e., $$\\\\frac{\\\\sqrt{3}}{4}a^{2}$$, <br>\r\n$$a = \\\\frac{\\\\sqrt{4\\\\times Area}}{\\\\sqrt{3}}\\\\approx 10.74$$ and then using the formula for height $$h = \\\\frac{\\\\sqrt{3}}{2}\\\\times 10.74\\\\approx 9.3$$ units, calculate the height.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We will first calculate the side of the equilateral triangle using the formula for area, i.e., $$\\\\frac{\\\\sqrt{3}}{4}a^{2}$$, <br>\r\n$$a = \\\\frac{\\\\sqrt{4\\\\times Area}}{\\\\sqrt{3}}\\\\approx 10.74$$ and then using the formula for height $$h = \\\\frac{\\\\sqrt{3}}{2}\\\\times 10.74\\\\approx 9.3$$ units, calculate the height.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the height of an equilateral triangle if its perimeter is 27 units.\",\n                    \"text\": \"Find the height of an equilateral triangle if its perimeter is 27 units.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$h = \\\\frac{Perimeter}{2\\\\sqrt{3}} = \\\\frac{27}{2\\\\sqrt{3}}\\\\approx 7.8\\\\; units$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$h = \\\\frac{Perimeter}{2\\\\sqrt{3}} = \\\\frac{27}{2\\\\sqrt{3}}\\\\approx 7.8\\\\; units$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"9 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$h = \\\\frac{Perimeter}{2\\\\sqrt{3}} = \\\\frac{27}{2\\\\sqrt{3}}\\\\approx 7.8\\\\; units$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$h = \\\\frac{Perimeter}{2\\\\sqrt{3}} = \\\\frac{27}{2\\\\sqrt{3}}\\\\approx 7.8\\\\; units$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"7.8 units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$h = \\\\frac{Perimeter}{2\\\\sqrt{3}} = \\\\frac{27}{2\\\\sqrt{3}}\\\\approx 7.8\\\\; units$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$h = \\\\frac{Perimeter}{2\\\\sqrt{3}} = \\\\frac{27}{2\\\\sqrt{3}}\\\\approx 7.8\\\\; units$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the height of an equilateral triangle if its area is 100 square units.\",\n                    \"text\": \"Find the height of an equilateral triangle if its area is 100 square units.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We will first calculate the side of the equilateral triangle using the formula for calculating the area.<br>\r\nArea $$=100=\\\\frac{\\\\sqrt{3}}{4}$$a$$^{2}$$<br>\r\n$$a=\\\\sqrt{\\\\frac{4 \\\\times Area}{ \\\\sqrt{3}}} \\\\approx 15.19$$ square units<br>\r\nNow use the formula for height.<br>\r\n$$h=\\\\frac{\\\\sqrt{3}}{2}\\\\times15.19\\\\approx13.16$$ units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"20.24 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will first calculate the side of the equilateral triangle using the formula for calculating the area.<br>\r\nArea $$=100=\\\\frac{\\\\sqrt{3}}{4}$$a$$^{2}$$<br>\r\n$$a=\\\\sqrt{\\\\frac{4 \\\\times Area}{ \\\\sqrt{3}}} \\\\approx 15.19$$ square units<br>\r\nNow use the formula for height.<br>\r\n$$h=\\\\frac{\\\\sqrt{3}}{2}\\\\times15.19\\\\approx13.16$$ units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"26.37 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will first calculate the side of the equilateral triangle using the formula for calculating the area.<br>\r\nArea $$=100=\\\\frac{\\\\sqrt{3}}{4}$$a$$^{2}$$<br>\r\n$$a=\\\\sqrt{\\\\frac{4 \\\\times Area}{ \\\\sqrt{3}}} \\\\approx 15.19$$ square units<br>\r\nNow use the formula for height.<br>\r\n$$h=\\\\frac{\\\\sqrt{3}}{2}\\\\times15.19\\\\approx13.16$$ units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"30.71 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We will first calculate the side of the equilateral triangle using the formula for calculating the area.<br>\r\nArea $$=100=\\\\frac{\\\\sqrt{3}}{4}$$a$$^{2}$$<br>\r\n$$a=\\\\sqrt{\\\\frac{4 \\\\times Area}{ \\\\sqrt{3}}} \\\\approx 15.19$$ square units<br>\r\nNow use the formula for height.<br>\r\n$$h=\\\\frac{\\\\sqrt{3}}{2}\\\\times15.19\\\\approx13.16$$ units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"13.16 units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We will first calculate the side of the equilateral triangle using the formula for calculating the area.<br>\r\nArea $$=100=\\\\frac{\\\\sqrt{3}}{4}$$a$$^{2}$$<br>\r\n$$a=\\\\sqrt{\\\\frac{4 \\\\times Area}{ \\\\sqrt{3}}} \\\\approx 15.19$$ square units<br>\r\nNow use the formula for height.<br>\r\n$$h=\\\\frac{\\\\sqrt{3}}{2}\\\\times15.19\\\\approx13.16$$ units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We will first calculate the side of the equilateral triangle using the formula for calculating the area.<br>\r\nArea $$=100=\\\\frac{\\\\sqrt{3}}{4}$$a$$^{2}$$<br>\r\n$$a=\\\\sqrt{\\\\frac{4 \\\\times Area}{ \\\\sqrt{3}}} \\\\approx 15.19$$ square units<br>\r\nNow use the formula for height.<br>\r\n$$h=\\\\frac{\\\\sqrt{3}}{2}\\\\times15.19\\\\approx13.16$$ units\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-frequently-asked-questions-on-height-of-equilateral-triangle\">Frequently Asked Questions On Height of Equilateral Triangle<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-128e96a1-20d9-4837-b9b9-41801b987311\" 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-0-128e96a1-20d9-4837-b9b9-41801b987311\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-128e96a1-20d9-4837-b9b9-41801b987311\"><strong>What is the formula to find the area 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-0-128e96a1-20d9-4837-b9b9-41801b987311\">\n\n<p class=\"eplus-wrapper\">The height of an equilateral triangle is given by the formula,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = \\frac{\\sqrt{3}}{2}a$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Where, a is the side length<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus using the formula for area of the triangle, i.e., half the product of base and height.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area $= \\frac{1}{2}\\times b\\times h$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area $= \\frac{1}{2} \\times a \\times \\frac{\\sqrt{3}}{2}a$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area $= \\frac{\\sqrt{3}}{4}a^{2}$<\/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-1-128e96a1-20d9-4837-b9b9-41801b987311\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-128e96a1-20d9-4837-b9b9-41801b987311\"><strong>Are the lengths of the heights drawn from all three vertices of an equilateral triangle equal or not?<\/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-1-128e96a1-20d9-4837-b9b9-41801b987311\">\n\n<p class=\"eplus-wrapper\">For an equilateral triangle the heights from all three vertices are equal, since the height depends on the side of an equilateral triangle, which is equal for all three sides of an equilateral 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-2-128e96a1-20d9-4837-b9b9-41801b987311\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-128e96a1-20d9-4837-b9b9-41801b987311\"><strong>Is the height of an equilateral triangle equal to the base of the 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-2-128e96a1-20d9-4837-b9b9-41801b987311\">\n\n<p class=\"eplus-wrapper\">Height of an equilateral triangle is not equal to the base of an equilateral triangle. It is a multiple of the side of an equilateral triangle, given as&nbsp; $h = \\frac{\\sqrt{3}}{2}a$.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What is the Height of an Equilateral Triangle? Height is a term that we use to describe how tall an object is when measured vertically. Height of an equilateral triangle is described as the length of the equilateral triangle measured from its top vertex to the base. Height of Equilateral Triangle: Definition&nbsp; An equilateral triangle &#8230; <a title=\"Height of Equilateral Triangle &#8211; Formula, Method, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/height-of-equilateral-triangle\" aria-label=\"More on Height of Equilateral Triangle &#8211; Formula, Method, 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-25883","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\/25883","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=25883"}],"version-history":[{"count":21,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25883\/revisions"}],"predecessor-version":[{"id":39937,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25883\/revisions\/39937"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=25883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=25883"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=25883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}