{"id":36485,"date":"2023-12-12T16:21:38","date_gmt":"2023-12-12T16:21:38","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=36485"},"modified":"2023-12-12T16:47:11","modified_gmt":"2023-12-12T16:47:11","slug":"base-area-of-a-triangular-prism-definition-formulas-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-triangular-prism","title":{"rendered":"Base Area of a Triangular Prism &#8211; Definition, Formulas, 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-6eea8f91-6d9b-4c4b-a166-758af0a0c377\" 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\/base-area-of-a-triangular-prism#0-what-is-the-base-area-of-a-triangular-prism>What Is the Base Area of a Triangular Prism?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-triangular-prism#1-base-area-of-a-triangular-prism-formulas>Base Area of a Triangular Prism Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-triangular-prism#2-how-to-calculate-the-base-area-of-a-triangular-prism>How to Calculate the Base Area of a Triangular Prism<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-triangular-prism#5-solved-examples-on-base-area-of-a-triangular-prism>Solved Examples on Base Area of a Triangular Prism<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-triangular-prism#6-practice-problems-on-base-area-of-a-triangular-prism>Practice Problems on Base Area of a Triangular Prism<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-triangular-prism#7-frequently-asked-questions-about-base-area-of-a-triangular-prism>Frequently Asked Questions about Base Area of a Triangular Prism<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-base-area-of-a-triangular-prism\">What Is the Base Area of a Triangular Prism?<\/h2>\n\n\n\n<p><strong>The area of the triangle located at the base of a triangular prism is referred to as the base area of a triangular prism. It is measured in square units.<\/strong><\/p>\n\n\n\n<p>A triangular prism is a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polyhedron\">polyhedron<\/a>. It has three rectangular sides (lateral faces) and two triangular faces (one is the base and the other is the top). The two triangular faces are <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-lines\">parallel<\/a> and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/congruent\">congruent<\/a>. The base area of a triangular prism is the area of the base <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\">triangle<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"619\" height=\"418\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/triangular-prism.png\" alt=\"Triangular prism\" class=\"wp-image-36488\" title=\"Triangular prism\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/triangular-prism.png 619w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/triangular-prism-300x203.png 300w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/figure>\n\n\n\n<p>Take a look at the net of a triangular prism, which clearly shows the three rectangular lateral faces and two triangular bases.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"614\" height=\"818\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/net-of-a-triangular-prism-showing-two-triangular-bases.png\" alt=\"Net of a triangular prism showing two triangular bases\" class=\"wp-image-36489\" title=\"Net of a triangular prism showing two triangular bases\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/net-of-a-triangular-prism-showing-two-triangular-bases.png 614w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/net-of-a-triangular-prism-showing-two-triangular-bases-225x300.png 225w\" sizes=\"auto, (max-width: 614px) 100vw, 614px\" \/><\/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-multiples-of-100-using-base-10-blocks\" 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\/add_sub_pv_add_multiples_100_model_pt.png\" alt=\"Add Multiples of 100 Using Base-10 Blocks 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 Multiples of 100 Using Base-10 Blocks 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\/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\/add-using-base-10-blocks\" 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\/add_sub_pv_add_2d_2d_model_pt.png\" alt=\"Add Using Base-10 blocks 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 Using Base-10 blocks 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\/choose-the-equivalent-value-based-on-place-value\" 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\/place_value_relate_value_diff_places_pt.png\" alt=\"Choose the Equivalent Value Based on Place Value 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\">Choose the Equivalent Value Based on Place Value 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\/compose-numbers-based-on-tens-and-ones\" 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\/place_value_compose_10s_1s_1_pt.png\" alt=\"Compose Numbers based on Tens and Ones 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\">Compose Numbers based on Tens and Ones 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\/count-in-tens-using-base-10-blocks\" 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\/place_value_count_10s_base_10_block_pt.png\" alt=\"Count in Tens using Base 10 Blocks 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\">Count in Tens using Base 10 Blocks 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\" id=\"1-base-area-of-a-triangular-prism-formulas\">Base Area of a Triangular Prism Formulas<\/h2>\n\n\n\n<p>To find the base area of a triangular prism, we must know different formulas for finding the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/area\">area<\/a> of a triangle. Let\u2019s discuss some important formulas that can be helpful in finding the base area of a triangular prism.<\/p>\n\n\n\n<p><strong>Base Area of a Triangular Prism Formula When the Lengths of Sides of the Triangle Are Given<\/strong><\/p>\n\n\n\n<p>If the length of the sides of a triangular prism&#8217;s base is known, then its base area can be determined by using Heron&#8217;s formula.<\/p>\n\n\n\n<p>Base area of a triangular prism = Area of the base triangle = A<\/p>\n\n\n\n<p>$A = \\sqrt{s(s &#8211; a)(s &#8211; b)(s &#8211; c)}$<\/p>\n\n\n\n<p>where&nbsp;<\/p>\n\n\n\n<p>a, b, and c are the lengths of the sides of the base triangle, and<\/p>\n\n\n\n<p>s = semiperimeter $= \\frac{a + b + c}{2}$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"525\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/base-area-of-a-triangular-prism-if-the-sides-of-its-triangle-are-given.png\" alt=\"Base area of a triangular prism if the sides of its triangle are given\" class=\"wp-image-36490\" title=\"Base area of a triangular prism if the sides of its triangle are given\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/base-area-of-a-triangular-prism-if-the-sides-of-its-triangle-are-given.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/base-area-of-a-triangular-prism-if-the-sides-of-its-triangle-are-given-300x254.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Base Area of a Triangular Prism Formula When the Base and Height of the Triangle Are Given<\/strong><\/p>\n\n\n\n<p>If the length of the base triangle and its height is known, then the base area of a triangular prism can be calculated as follows:&nbsp;<\/p>\n\n\n\n<p>Base area of a triangular prism = Area of the triangular base<\/p>\n\n\n\n<p>If the base \u201cb\u201d and height \u201ch\u201d of the base triangle is given, then the base area of the triangular prism $= \\frac{1}{2} \\times b \\times h$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"456\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/base-area-of-a-triangular-prism-formula-if-the-base-and-height-of-the-triangle-are-given.png\" alt=\"Base area of a triangular prism formula if the base and height of the triangle are given\" class=\"wp-image-36491\" title=\"Base area of a triangular prism formula if the base and height of the triangle are given\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/base-area-of-a-triangular-prism-formula-if-the-base-and-height-of-the-triangle-are-given.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/12\/base-area-of-a-triangular-prism-formula-if-the-base-and-height-of-the-triangle-are-given-300x221.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Let\u2019s summarize!<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td colspan=\"2\"><strong>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Triangular Prism Base Area Formulas<\/strong><\/td><\/tr><tr><td><strong>What do we know about the base triangle?<\/strong><\/td><td><strong>Formula<\/strong><\/td><\/tr><tr><td>&nbsp; &nbsp; &nbsp; Equilateral Triangle<\/td><td>\u00a0 \u00a0 $A = \\frac{\\sqrt{3}}{4} \\times a^{2}$<\/td><\/tr><tr><td>&nbsp; &nbsp; &nbsp; Base = b, Height = h<\/td><td>\u00a0 \u00a0 $A = \\frac{1}{2} \\times b \\times h$<\/td><\/tr><tr><td>&nbsp; Side-lengths: a, b, c, and semiperimeter s<\/td><td>\u00a0 \u00a0 $A = \\sqrt{s(s &#8211; a)(s &#8211; b)(s &#8211; c)}$<\/td><\/tr><\/tbody><\/table><\/figure>\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    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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\" id=\"2-how-to-calculate-the-base-area-of-a-triangular-prism\">How to Calculate the Base Area of a Triangular Prism<\/h2>\n\n\n\n<p>We can determine the base area of a triangular prism by finding the area of the base triangle. Depending on the known parameters and type of triangle in the base, various formulas can be used to determine the area of the base of a triangular prism.&nbsp;<\/p>\n\n\n\n<p>Let&#8217;s see how to calculate the base area of a triangular prism.&nbsp;<\/p>\n\n\n\n<p><strong>Equilateral Triangle<\/strong><\/p>\n\n\n\n<p>If the base triangle is an equilateral triangle and each side length is \u201ca,\u201d then the base area of the triangular prism is given by&nbsp;<\/p>\n\n\n\n<p>$Area = \\frac{\\sqrt{3}}{4} \\times a^{2}$<\/p>\n\n\n\n<p><strong>Triangle with base b and height h<\/strong><\/p>\n\n\n\n<p>If the base \u201cb\u201d and height \u201ch\u201d of the base triangle are given, then the base area of the triangular prism can be calculated as&nbsp;<\/p>\n\n\n\n<p>$A = \\frac{1}{2} \\times b \\times h$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-facts-about-the-base-area-of-a-triangular-prism\">Facts about the Base Area of a Triangular Prism<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>A triangular prism has two triangular bases and three rectangular sides (lateral faces).<\/li>\n\n\n\n<li>The triangular prism is said to be semiregular if the bases are equilateral triangles and the other faces are squares rather than rectangles.<\/li>\n\n\n\n<li>The total surface area of a triangular prism is the sum of the areas of the two triangular bases and the lateral surface area.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we have learned about the base area of a triangular prism for the different types of triangular bases. We discussed important formulas for finding the base area of a triangular prism. Let\u2019s use these formulas to solve a few examples and practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-solved-examples-on-base-area-of-a-triangular-prism\">Solved Examples on Base Area of a Triangular Prism<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>What is the base area of a triangular prism if the right triangle at its base has the base = 3 units and height = 4 units?<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The base of the given triangular prism is a right triangle whose base is 3 units and height 4 units.<\/p>\n\n\n\n<p>Area of triangle with base b and height $h = \\frac{1}{2} \\times b \\times h$<\/p>\n\n\n\n<p>Base area of triangular prism $= \\frac{1}{2} \\times 3 \\times 4$<\/p>\n\n\n\n<p>Base area of triangular prism = 6 square units<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>Find the base area of the triangular prism whose sides are 3 inches, 4 inches, and 5 inches respectively.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>a = 3 inches, b = 4 inches and c = 5 inches<\/p>\n\n\n\n<p>Using the Heron&#8217;s formula, we write<\/p>\n\n\n\n<p>Area of triangle $= \\sqrt{s(s &#8211; a)(s &#8211; b)(s &#8211; c)}$<\/p>\n\n\n\n<p>Semiperimeter $(s) = \\frac{a + b + c}{2} = \\frac{3 + 4 + 5}{2} = \\frac{12}{2} = 6$ inches<\/p>\n\n\n\n<p>Substituting the values of s, a, b, and c in the above formula, we get<\/p>\n\n\n\n<p>Area of triangle $= \\sqrt{6(6 &#8211; 3)(6 &#8211; 4)(6 &#8211; 5)}$<\/p>\n\n\n\n<p>Area of triangle $= \\sqrt{6 \\times 3 \\times 2 \\times 1} = \\sqrt{6 \\times 6} = 6$ square inches<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>If the height of the triangular base of a triangular prism is 5 inches and the base length is 12 inches, find the base area of the triangular prism.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>h = 5 inches and b = 12 inches<\/p>\n\n\n\n<p>Area of the triangle when height and base side are given $= \\frac{1}{2} \\times b \\times h$<\/p>\n\n\n\n<p>\u2234 Area of triangle $= \\frac{1}{2} \\times 12 \\times 5 = 30$ square inches<\/p>\n\n\n\n<p>Base area = 30 square inches<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li><strong>If the base area of a triangular prism is <\/strong>$180 \\;inch^{2}$<strong> and the base length is 9 inches, then find the height of the triangular base.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>The base area of a triangular prism=180 inch2 and b=9 inches<\/p>\n\n\n\n<p>The base area of a triangular prism $= \\frac{1}{2} \\times b \\times h$<\/p>\n\n\n\n<p>$\\Rightarrow \\frac{1}{2} \\times 9 \\times h = 180$<\/p>\n\n\n\n<p>$\\Rightarrow h = \\frac{180 \\times 2}{9} = 40$ inches<\/p>\n\n\n\n<p>Hence, the height of the triangular bases is 40 inches.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li><strong>If the base of a triangular prism is an equilateral triangle and the perimeter of the base is 120 feet, find the base area of the prism.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Let the side of equilateral triangle $= a$<\/p>\n\n\n\n<p>Perimeter $= 120$ feet<\/p>\n\n\n\n<p>$\\Rightarrow a + a + a = 120$<\/p>\n\n\n\n<p>$\\Rightarrow a = 40$ feet<\/p>\n\n\n\n<p>Area of triangle $= \\frac{\\sqrt{3} a^{2}}{4}$<\/p>\n\n\n\n<p>Area of triangle $= \\frac{\\sqrt{3}}{4} \\times 40 \\times 40 = 400\\sqrt{3}$ square feet<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"6\">\n<li><strong>The base sides of a triangular prism are in the ratio 7 : 5 : 10 and its perimeter is 22 units. Find the base area of the triangular prism.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let the sides be 7x, 5x, and 10x.<\/p>\n\n\n\n<p>Perimeter $= 7x + 5x + 10x = 22$<\/p>\n\n\n\n<p>$\\Rightarrow 22x = 22$<\/p>\n\n\n\n<p>$\\Rightarrow x = 1$<\/p>\n\n\n\n<p>Therefore, we get the values<\/p>\n\n\n\n<p>a = 7 , b = 5, c = 10<\/p>\n\n\n\n<p>$s = \\frac{a + b + c}{2} = \\frac{22}{2} = 11$ inches<\/p>\n\n\n\n<p>\u2234\u00a0 Area of triangle $= \\sqrt{11(11 &#8211; 7)(11 &#8211; 5)(11 &#8211; 10)}$<\/p>\n\n\n\n<p>\u2234\u00a0 Area of triangle $= \\sqrt{11 \\times 4 \\times 6 \\times 1}$<\/p>\n\n\n\n<p>\u2234\u00a0 Area of triangle $= 2\\sqrt{66}$ square units<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-practice-problems-on-base-area-of-a-triangular-prism\">Practice Problems on Base Area of a Triangular Prism<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Base Area of a Triangular Prism - Definition, Formulas, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">A triangular prism has ______ triangular faces.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">3<\/div><div class=\"spq_answer_block\" data-value=\"3\">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: 2<br\/>A triangular prism has two triangular faces (one at the top and the other at the bottom).<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The base area of the triangular prism whose base-edges are x units, y units, and z units is ______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{2} (x + y + z)$ square units<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{1}{2} xy$ square units<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\sqrt{s(s - x)(s - y)(s - z)}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{1}{3} xyz$ square 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: $\\sqrt{s(s - x)(s - y)(s - z)}$<br\/>Area of the triangular prism whose triangular base has edges x units, y units, and z units is given by Heron's formula.<br>\r\n$A = \\sqrt{s(s - x)(s - y)(s - z)}$ square units<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If the base-edge of the triangular base of the triangular prism is 24 inches and its base area is 60 square units, then the height of the triangle is _______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5 units<\/div><div class=\"spq_answer_block\" data-value=\"1\">8 units<\/div><div class=\"spq_answer_block\" data-value=\"2\">4 units<\/div><div class=\"spq_answer_block\" data-value=\"3\">3 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: 5 units<br\/>Area of the triangle when height and base side are given$= \\frac{1}{2} \\times b \\times h$<br>\r\n$\\Rightarrow \\frac{1}{2} \\times 24 \\times h = 60$<br>\r\n$\\Rightarrow h = \\frac{60}{12} = 5$ units<\/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 sides of the triangular base of a prism are 10 units, 12 units, and 6 units, then the base area is equal to ___________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$9\\sqrt{19}$ square units<\/div><div class=\"spq_answer_block\" data-value=\"1\">$8\\sqrt{14}$ square units<\/div><div class=\"spq_answer_block\" data-value=\"2\">$6\\sqrt{11}$ square units<\/div><div class=\"spq_answer_block\" data-value=\"3\">$11\\sqrt{17}$ square 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: $8\\sqrt{14}$ square units<br\/>Sides of the triangular base of a prism are 10 units, 12 units, and 6 units.<br>\r\nHere, $s = \\frac{a + b + c}{2} = \\frac{28}{2} = 14$<br>\r\n\u2234 Base areas of triangular prism $= \\sqrt{14(14 - 10)(14 - 12)(14 - 6)}$<br>\r\n$= \\sqrt{14 \\times 4 \\times 2 \\times 8}$<br>\r\n$= 8\\sqrt{14}$ square units<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">If the base of a triangular prism is an equilateral triangle with a side length of 16 inches. Then the base area of the prism is _______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$4\\sqrt{3}\\; inch^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$16\\sqrt{3}\\; inch^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$32\\sqrt{3}\\; inch^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$64\\sqrt{3}\\; inch^{2}$<\/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: $64\\sqrt{3}\\; inch^{2}$<br\/>If the base triangle is equilateral and each side length is \u201ca,\u201d then the base area of the triangular prism $= \\frac{\\sqrt{3}}{4} \\times a^{2}$<br>\r\n$A = \\frac{\\sqrt{3}}{4} \\times 16 \\times 16$<br>\r\n$A = 64\\sqrt{3}\\; inch^{2}$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": 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triangular prism has ______ triangular faces.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A triangular prism has two triangular faces (one at the top and the other at the bottom).\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangular prism has two triangular faces (one at the top and the other at the bottom).\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangular prism has two triangular faces (one at the top and the other at the bottom).\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangular prism has two triangular faces (one at the top and the other at the bottom).\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"2\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A triangular prism has two triangular faces (one at the top and the other at the bottom).\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A triangular prism has two triangular faces (one at the top and the other at the bottom).\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The base area of the triangular prism whose base-edges are x units, y units, and z units is ______.\",\n                    \"text\": \"The base area of the triangular prism whose base-edges are x units, y units, and z units is ______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Area of the triangular prism whose triangular base has edges x units, y units, and z units is given by Heron's formula.<br>\r\n$$A = \\\\sqrt{s(s - x)(s - y)(s - z)}$$ square units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{2} (x + y + z)$$ square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of the triangular prism whose triangular base has edges x units, y units, and z units is given by Heron's formula.<br>\r\n$$A = \\\\sqrt{s(s - x)(s - y)(s - z)}$$ square units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{2} xy$$ square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of the triangular prism whose triangular base has edges x units, y units, and z units is given by Heron's formula.<br>\r\n$$A = \\\\sqrt{s(s - x)(s - y)(s - z)}$$ square units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{3} xyz$$ square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of the triangular prism whose triangular base has edges x units, y units, and z units is given by Heron's formula.<br>\r\n$$A = \\\\sqrt{s(s - x)(s - y)(s - z)}$$ square units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\sqrt{s(s - x)(s - y)(s - z)}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Area of the triangular prism whose triangular base has edges x units, y units, and z units is given by Heron's formula.<br>\r\n$$A = \\\\sqrt{s(s - x)(s - y)(s - z)}$$ square units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Area of the triangular prism whose triangular base has edges x units, y units, and z units is given by Heron's formula.<br>\r\n$$A = \\\\sqrt{s(s - x)(s - y)(s - z)}$$ square units\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the base-edge of the triangular base of the triangular prism is 24 inches and its base area is 60 square units, then the height of the triangle is _______.\",\n                    \"text\": \"If the base-edge of the triangular base of the triangular prism is 24 inches and its base area is 60 square units, then the height of the triangle is _______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Area of the triangle when height and base side are given$$= \\\\frac{1}{2} \\\\times b \\\\times h$$<br>\r\n$$\\\\Rightarrow \\\\frac{1}{2} \\\\times 24 \\\\times h = 60$$<br>\r\n$$\\\\Rightarrow h = \\\\frac{60}{12} = 5$$ 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\": \"Area of the triangle when height and base side are given$$= \\\\frac{1}{2} \\\\times b \\\\times h$$<br>\r\n$$\\\\Rightarrow \\\\frac{1}{2} \\\\times 24 \\\\times h = 60$$<br>\r\n$$\\\\Rightarrow h = \\\\frac{60}{12} = 5$$ units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of the triangle when height and base side are given$$= \\\\frac{1}{2} \\\\times b \\\\times h$$<br>\r\n$$\\\\Rightarrow \\\\frac{1}{2} \\\\times 24 \\\\times h = 60$$<br>\r\n$$\\\\Rightarrow h = \\\\frac{60}{12} = 5$$ units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of the triangle when height and base side are given$$= \\\\frac{1}{2} \\\\times b \\\\times h$$<br>\r\n$$\\\\Rightarrow \\\\frac{1}{2} \\\\times 24 \\\\times h = 60$$<br>\r\n$$\\\\Rightarrow h = \\\\frac{60}{12} = 5$$ units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5 units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Area of the triangle when height and base side are given$$= \\\\frac{1}{2} \\\\times b \\\\times h$$<br>\r\n$$\\\\Rightarrow \\\\frac{1}{2} \\\\times 24 \\\\times h = 60$$<br>\r\n$$\\\\Rightarrow h = \\\\frac{60}{12} = 5$$ units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Area of the triangle when height and base side are given$$= \\\\frac{1}{2} \\\\times b \\\\times h$$<br>\r\n$$\\\\Rightarrow \\\\frac{1}{2} \\\\times 24 \\\\times h = 60$$<br>\r\n$$\\\\Rightarrow h = \\\\frac{60}{12} = 5$$ units\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the sides of the triangular base of a prism are 10 units, 12 units, and 6 units, then the base area is equal to ___________.\",\n                    \"text\": \"If the sides of the triangular base of a prism are 10 units, 12 units, and 6 units, then the base area is equal to ___________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Sides of the triangular base of a prism are 10 units, 12 units, and 6 units.<br>\r\nHere, $$s = \\\\frac{a + b + c}{2} = \\\\frac{28}{2} = 14$$<br>\r\n\u2234 Base areas of triangular prism $$= \\\\sqrt{14(14 - 10)(14 - 12)(14 - 6)}$$<br>\r\n$$= \\\\sqrt{14 \\\\times 4 \\\\times 2 \\\\times 8}$$<br>\r\n$$= 8\\\\sqrt{14}$$ square units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$9\\\\sqrt{19}$$ square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sides of the triangular base of a prism are 10 units, 12 units, and 6 units.<br>\r\nHere, $$s = \\\\frac{a + b + c}{2} = \\\\frac{28}{2} = 14$$<br>\r\n\u2234 Base areas of triangular prism $$= \\\\sqrt{14(14 - 10)(14 - 12)(14 - 6)}$$<br>\r\n$$= \\\\sqrt{14 \\\\times 4 \\\\times 2 \\\\times 8}$$<br>\r\n$$= 8\\\\sqrt{14}$$ square units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$6\\\\sqrt{11}$$ square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sides of the triangular base of a prism are 10 units, 12 units, and 6 units.<br>\r\nHere, $$s = \\\\frac{a + b + c}{2} = \\\\frac{28}{2} = 14$$<br>\r\n\u2234 Base areas of triangular prism $$= \\\\sqrt{14(14 - 10)(14 - 12)(14 - 6)}$$<br>\r\n$$= \\\\sqrt{14 \\\\times 4 \\\\times 2 \\\\times 8}$$<br>\r\n$$= 8\\\\sqrt{14}$$ square units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$11\\\\sqrt{17}$$ square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sides of the triangular base of a prism are 10 units, 12 units, and 6 units.<br>\r\nHere, $$s = \\\\frac{a + b + c}{2} = \\\\frac{28}{2} = 14$$<br>\r\n\u2234 Base areas of triangular prism $$= \\\\sqrt{14(14 - 10)(14 - 12)(14 - 6)}$$<br>\r\n$$= \\\\sqrt{14 \\\\times 4 \\\\times 2 \\\\times 8}$$<br>\r\n$$= 8\\\\sqrt{14}$$ square units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$8\\\\sqrt{14}$$ square units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Sides of the triangular base of a prism are 10 units, 12 units, and 6 units.<br>\r\nHere, $$s = \\\\frac{a + b + c}{2} = \\\\frac{28}{2} = 14$$<br>\r\n\u2234 Base areas of triangular prism $$= \\\\sqrt{14(14 - 10)(14 - 12)(14 - 6)}$$<br>\r\n$$= \\\\sqrt{14 \\\\times 4 \\\\times 2 \\\\times 8}$$<br>\r\n$$= 8\\\\sqrt{14}$$ square units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Sides of the triangular base of a prism are 10 units, 12 units, and 6 units.<br>\r\nHere, $$s = \\\\frac{a + b + c}{2} = \\\\frac{28}{2} = 14$$<br>\r\n\u2234 Base areas of triangular prism $$= \\\\sqrt{14(14 - 10)(14 - 12)(14 - 6)}$$<br>\r\n$$= \\\\sqrt{14 \\\\times 4 \\\\times 2 \\\\times 8}$$<br>\r\n$$= 8\\\\sqrt{14}$$ square units\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the base of a triangular prism is an equilateral triangle with a side length of 16 inches. Then the base area of the prism is _______.\",\n                    \"text\": \"If the base of a triangular prism is an equilateral triangle with a side length of 16 inches. Then the base area of the prism is _______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If the base triangle is equilateral and each side length is \u201ca,\u201d then the base area of the triangular prism $$= \\\\frac{\\\\sqrt{3}}{4} \\\\times a^{2}$$<br>\r\n$$A = \\\\frac{\\\\sqrt{3}}{4} \\\\times 16 \\\\times 16$$<br>\r\n$$A = 64\\\\sqrt{3}\\\\; inch^{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$4\\\\sqrt{3}\\\\; inch^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the base triangle is equilateral and each side length is \u201ca,\u201d then the base area of the triangular prism $$= \\\\frac{\\\\sqrt{3}}{4} \\\\times a^{2}$$<br>\r\n$$A = \\\\frac{\\\\sqrt{3}}{4} \\\\times 16 \\\\times 16$$<br>\r\n$$A = 64\\\\sqrt{3}\\\\; inch^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$16\\\\sqrt{3}\\\\; inch^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the base triangle is equilateral and each side length is \u201ca,\u201d then the base area of the triangular prism $$= \\\\frac{\\\\sqrt{3}}{4} \\\\times a^{2}$$<br>\r\n$$A = \\\\frac{\\\\sqrt{3}}{4} \\\\times 16 \\\\times 16$$<br>\r\n$$A = 64\\\\sqrt{3}\\\\; inch^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$32\\\\sqrt{3}\\\\; inch^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the base triangle is equilateral and each side length is \u201ca,\u201d then the base area of the triangular prism $$= \\\\frac{\\\\sqrt{3}}{4} \\\\times a^{2}$$<br>\r\n$$A = \\\\frac{\\\\sqrt{3}}{4} \\\\times 16 \\\\times 16$$<br>\r\n$$A = 64\\\\sqrt{3}\\\\; inch^{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$64\\\\sqrt{3}\\\\; inch^{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If the base triangle is equilateral and each side length is \u201ca,\u201d then the base area of the triangular prism $$= \\\\frac{\\\\sqrt{3}}{4} \\\\times a^{2}$$<br>\r\n$$A = \\\\frac{\\\\sqrt{3}}{4} \\\\times 16 \\\\times 16$$<br>\r\n$$A = 64\\\\sqrt{3}\\\\; inch^{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If the base triangle is equilateral and each side length is \u201ca,\u201d then the base area of the triangular prism $$= \\\\frac{\\\\sqrt{3}}{4} \\\\times a^{2}$$<br>\r\n$$A = \\\\frac{\\\\sqrt{3}}{4} \\\\times 16 \\\\times 16$$<br>\r\n$$A = 64\\\\sqrt{3}\\\\; inch^{2}$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-frequently-asked-questions-about-base-area-of-a-triangular-prism\">Frequently Asked Questions about Base Area of a Triangular Prism<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-a6fb490d-9344-4406-ad90-73759d844d52\" 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-a6fb490d-9344-4406-ad90-73759d844d52\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a6fb490d-9344-4406-ad90-73759d844d52\"><strong>What is the number of triangles and rectangles in a triangular prism?<\/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-a6fb490d-9344-4406-ad90-73759d844d52\">\n\n<p>A triangular prism is made of two triangles and three rectangles.<\/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-a6fb490d-9344-4406-ad90-73759d844d52\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a6fb490d-9344-4406-ad90-73759d844d52\"><strong>What do you mean by the scalene triangular base of a prism?<\/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-a6fb490d-9344-4406-ad90-73759d844d52\">\n\n<p>If the base triangle of a prism has all sides of different lengths, it is a scalene 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-a6fb490d-9344-4406-ad90-73759d844d52\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a6fb490d-9344-4406-ad90-73759d844d52\"><strong>What do you mean by the base area of a triangular prism?<\/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-a6fb490d-9344-4406-ad90-73759d844d52\">\n\n<p>The region or area that is covered by the base of a triangular prism is known as the base area.<\/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-a6fb490d-9344-4406-ad90-73759d844d52\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a6fb490d-9344-4406-ad90-73759d844d52\"><strong>What is the base area of a triangular prism if the base is 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-3-a6fb490d-9344-4406-ad90-73759d844d52\">\n\n<p>If the base triangle is equilateral and each side length is \u201ca,\u201d then the base area of the triangular prism $= \\frac{\\sqrt{3}}{4} \\times a^{2}$.<\/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-4-a6fb490d-9344-4406-ad90-73759d844d52\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a6fb490d-9344-4406-ad90-73759d844d52\"><strong>How do you find the base area of a triangular prism?<\/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-a6fb490d-9344-4406-ad90-73759d844d52\">\n\n<p>To find the base area of a triangular prism, find the area of the triangle at its base.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Base Area of a Triangular Prism? The area of the triangle located at the base of a triangular prism is referred to as the base area of a triangular prism. It is measured in square units. A triangular prism is a polyhedron. It has three rectangular sides (lateral faces) and two triangular &#8230; <a title=\"Base Area of a Triangular Prism &#8211; Definition, Formulas, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-triangular-prism\" aria-label=\"More on Base Area of a Triangular Prism &#8211; Definition, Formulas, 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-36485","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\/36485","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=36485"}],"version-history":[{"count":8,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36485\/revisions"}],"predecessor-version":[{"id":36499,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36485\/revisions\/36499"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=36485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=36485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=36485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}