{"id":26036,"date":"2023-03-09T05:51:30","date_gmt":"2023-03-09T05:51:30","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26036"},"modified":"2024-02-05T15:27:07","modified_gmt":"2024-02-05T15:27:07","slug":"volume-of-a-triangular-pyramid-definition-example-facts","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-triangular-pyramid","title":{"rendered":"Volume of a Triangular Pyramid: Definition, Example, Facts"},"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-0afb7139-f98a-4c22-b8a1-5634ac236827\" 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\/volume-of-triangular-pyramid#0-what-is-the-volume-of-a-triangular-pyramid>What Is The Volume of a Triangular Pyramid?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-triangular-pyramid#2-the-formula-for-the-volume-of-a-triangular-pyramid>The Formula for the Volume of a Triangular Pyramid<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-triangular-pyramid#3-how-to-find-the-volume-of-a-triangular-pyramid>How to Find the Volume of a Triangular Pyramid<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-triangular-pyramid#6-solved-examples-for-the-volume-of-a-triangular-pyramid>Solved Examples for the Volume of a Triangular Pyramid<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-triangular-pyramid#7-practice-problems-on-the-volume-of-a-triangular-pyramid>Practice Problems on the Volume of a Triangular Pyramid<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-triangular-pyramid#8-frequently-asked-questions-on-the-volume-of-a-triangular-pyramid>Frequently Asked Questions on the Volume of a Triangular Pyramid<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-volume-of-a-triangular-pyramid\">What Is The Volume of a Triangular Pyramid?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s imagine you are making homemade chocolate and want to shape it somewhat like Toblerone. You go to the market and buy a triangular pyramid-shaped setting mold. You will need to work out the volume of the triangular pyramid-shaped mold to find the amount of chocolate you need to put into it.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, what\u2019s volume? Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object. Volume of a triangular pyramid is the volume of a pyramid with a triangular base.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"388\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-triangular-pyramid-shaped-chocolate.png\" alt=\"A triangular pyramid shaped chocolate\" class=\"wp-image-37293\" title=\"A triangular pyramid shaped chocolate\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-triangular-pyramid-shaped-chocolate.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-triangular-pyramid-shaped-chocolate-300x188.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/estimate-the-volume-of-a-given-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\/geo_meas_estimate_vol_1_pt.png\" alt=\"Estimate the Volume of a Given 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\">Estimate the Volume of a Given 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\/find-the-volume-of-the-3d-shape-by-iterating\" 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_iterate_vol_1_pt.png\" alt=\"Find the Volume of the 3D Shape by Iterating Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Volume of the 3D Shape by Iterating Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-volume-using-unit-cubes\" 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_vol_unit_cubes_2_pt.png\" alt=\"Find the Volume using Unit Cubes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Volume using Unit Cubes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-volume-using-the-formula\" 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_vol_formula_pt.png\" alt=\"Find Volume using the Formula Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Volume using the Formula 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\/introduction-to-volume\" 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_vol_unit_cubes_1_pt.png\" alt=\"Introduction to Volume 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\">Introduction to Volume 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\/iterate-and-find-the-total-volume\" 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_iterate_vol_2_pt.png\" alt=\"Iterate and Find the Total Volume 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\">Iterate and Find the Total Volume 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\/solve-the-word-problems-related-to-volume\" 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_vol_word_prob_pt.png\" alt=\"Solve the Word Problems Related to Volume 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\">Solve the Word Problems Related to Volume 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\/use-the-3d-shapes-to-estimate-the-volume\" 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_estimate_vol_2_pt.png\" alt=\"Use the 3D Shapes to Estimate the Volume 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\">Use the 3D Shapes to Estimate the Volume 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=\"1-triangular-pyramid-and-its-parts\">Triangular Pyramid and Its Parts<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A triangular pyramid is a three-dimensional shape with flat triangular faces, straight edges, and sharp corners or vertices. It is made up of three triangular faces and a triangular base. It has four faces, six edges, and four vertices.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If all four faces of a triangular pyramid are equilateral triangles, then it is called a regular triangular pyramid.<br><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"444\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/parts-of-triangular-pyramid-and-a-regular-triangular-pyramid.png\" alt=\"Parts of triangular pyramid and a regular triangular pyramid\" class=\"wp-image-37295\" title=\"Parts of triangular pyramid and a regular triangular pyramid\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/parts-of-triangular-pyramid-and-a-regular-triangular-pyramid.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/parts-of-triangular-pyramid-and-a-regular-triangular-pyramid-300x215.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Now that we know what a triangular pyramid is, let\u2019s look at how to find the volume of a triangular pyramid.<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-the-number-pyramid\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/complete-the-number-pyramid.jpeg\" alt=\"Complete the Number Pyramid 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\/fill-the-number-pyramid\" 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\/fill-the-number-pyramid.jpeg\" alt=\"Fill the Number Pyramid 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\/subtract-to-complete-the-number-pyramid\" 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\/subtract-to-complete-the-number-pyramid.jpeg\" alt=\"Subtract to Complete the Number Pyramid 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=\"2-the-formula-for-the-volume-of-a-triangular-pyramid\">The Formula for the Volume of a Triangular Pyramid<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The volume of a triangular pyramid is one-third times the product of the area of the base triangle and the height of the pyramid. The triangular pyramid volume formula is<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$V = \\frac{1}{3} \\times B \\times h$ cubic units<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, <em>V<\/em> is the volume, <em>B<\/em> is the base area, and <em>h<\/em> is the height of the pyramid.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"464\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/volume-of-a-triangular-pyramid.png\" alt=\"Volume of a triangular pyramid\" class=\"wp-image-37296\" title=\"Volume of a triangular pyramid\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/volume-of-a-triangular-pyramid.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/volume-of-a-triangular-pyramid-300x225.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Note:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The formula for a regular triangular pyramid volume is:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$V = \\frac{a^{3}}{6\\sqrt{2}}$ cubic units<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Where <em>V<\/em> is the volume of the regular triangular pyramid, and <em>a <\/em>is the side of the equilateral triangle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-how-to-find-the-volume-of-a-triangular-pyramid\">How to Find the Volume of a Triangular Pyramid<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Now that we know the formula, we can find the volume of any triangular pyramid.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">First, we need to know if the given triangular pyramid is a regular triangular pyramid or not.&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If it is not a regular triangular pyramid then we use the following formula:<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$V = \\frac{1}{3} \\times Area of base \\times h$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Find the area of the base of the triangle.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">The area of a triangle is half of the product of the base of the triangle and the height of the triangle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$A = \\frac{1}{2} \\times b \\times h$&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, <em>A<\/em> is the area of a triangle, <em>b <\/em>is the base of the triangle, and <em>h <\/em>is the height of the triangle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If the base triangle is an equilateral triangle with the side <em>\u201ca\u2019<\/em>\u2019<em> <\/em>then we can find its area with the following formula:<br>$A = \\frac{\\sqrt{3}}{4} \\times a^{2}$<br>Here, <em>A<\/em> is the area of a triangle, and <em>a <\/em>is the side of the equilateral triangle.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Now, plug in the values of the area of the base and height in the formula mentioned earlier and simplify. The result is the volume of the triangular pyramid.&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If it is a regular triangular pyramid then use the following formula:<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$V = \\frac{a^{3}}{6\\sqrt{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Remember to write the unit! Volume is measured in cubic units.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-facts-about-the-volume-of-a-triangular-pyramid\">Facts about the Volume of a Triangular Pyramid<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">A regular triangular pyramid is also called a tetrahedron.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The volume of a triangular pyramid is represented in cubic units or another format of writing cubic unit as this is commonly used (unit)\u00b3, such as cubic centimeters, cubic inch, cubic foot, cubic meter, etc.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">A Rubik\u2019s triangle is an example of a triangular pyramid.<br><strong><\/strong><br>Image alt text: Triangular pyramid: real-life example<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The volume of a triangular pyramid is an important concept for learners. This can be better understood with practical examples. Using SplashLearn, students can practice each example with online interactive worksheets. This game-based learning app makes learning fun and keeps your child engaged.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-solved-examples-for-the-volume-of-a-triangular-pyramid\">Solved Examples for the Volume of a Triangular Pyramid<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. What is the volume of a triangular pyramid if its base area is 19 sq. inches and its height is 1.5 inches?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">It is given that base area $B = 19$ sq. inches and height of the pyramid $= 1.5$ inches.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know Volume $= \\frac{1}{3} \\times B \\times h$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting the values we get,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$Volume = \\frac{1}{3} \\times 19 \\times 1.5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$Volume = 19 \\times 0.5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$Volume = 9.5\\; cubic\\; inches$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Find the height of a triangular pyramid with a base area of 175 sq. units and a volume of 1050 cubic units.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">It is given that B $= 175$ and V $= 1050$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Volume of a triangular pyramid $= \\frac{1}{3} \\times B \\times h$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1050 = \\frac{1}{3} \\times 175 \\times h$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Rearranging the values we get,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = \\frac{3 \\times 1050}{175}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h = 18\\; units$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the height of the pyramid is 18 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. What is the volume of a regular triangular pyramid with a side of length <\/strong><strong>9<\/strong><strong>2 <\/strong><strong>units?&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">It is given that the side of a regular triangular pyramid i.e. $a = 9\\sqrt{2}$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that the volume of a regular triangular pyramid is&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$V = \\frac{a^{3}}{6\\sqrt{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting \u201c<em>a<\/em>\u201d as $9\\sqrt{2}$ we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$V = \\frac{(9\\sqrt{2})^{3}}{6\\sqrt{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$V = \\frac{9\\sqrt{2}&nbsp;\\times 9\\sqrt{2} \\times 9\\sqrt{2}}{6\\sqrt{2}} = 243$ cubic units<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the volume of the regular triangular pyramid is 243 cubic units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. Find the height of a regular triangular pyramid having a volume <\/strong>$18\\sqrt{2}$<strong> cubic units.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">It is given that the volume of a regular triangular pyramid, i.e., $V = 18\\sqrt{2}$ cubic units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that the volume of a regular triangular pyramid is:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$V = \\frac{a^{3}}{6\\sqrt{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting <em>\u201cV<\/em>\u201d as $18\\sqrt{2}$ we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$18\\sqrt{2} = \\frac{(a)^{3}}{6\\sqrt{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a^{3} = 18\\sqrt{2} \\times 6\\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a^{3} = 216$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Taking a cube root on both sides, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a = 6$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the height of the regular triangular pyramid is 6 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. Find the percentage change in the height of a triangular pyramid if its volume was increased to 75 cubic ft from 50 cubic ft, keeping the area of the base the same.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let the volume before increasing the height be V1 and the volume after increasing the height be $V_{2}$ .<\/p>\n\n\n\n<p class=\"eplus-wrapper\">It is given that $V_{1} = 50$ and $V_{2} = 75$ .<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know, Volume$= \\frac{1}{3} \\times B \\times h$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, $V_{1} = \\frac{1}{3} \\times B \\times h_{1} = 50$ and $V_{2} = \\frac{1}{3} \\times B \\times h_{2} = 75$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To find the percentage change in <em>h, <\/em>we need to find $\\frac{h_{2}}{h_{1}} \\times 100$. For this, we need to divide $V_{2}$ by $V_{1}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{V_{2}}{V_{1}} = \\frac{^{\\frac{1}{3} \\times B \\times h_{2}}}{^{\\frac{1}{3} \\times B \\times h_{1}}} = \\frac{75}{50}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{h_{2}}{h_{1}} = \\frac{3}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiplying both sides by 100.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{h_{2}}{h_{1}} \\times 100 = \\frac{3}{2} \\times 100$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{h2}{h1} \\times 100 = 1.5 \\times 100 = 150\\%$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the percentage increase in height is $150\\%$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-practice-problems-on-the-volume-of-a-triangular-pyramid\">Practice Problems on the Volume of a Triangular Pyramid<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Volume of a Triangular Pyramid: Definition, Example, Facts<\/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\">Choose the correct formula to determine the volume of a triangular pyramid.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$V = \\frac{1}{6} \\times B \\times h$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$V = \\frac{1}{3} \\times B \\times h$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$V = 3 \\times B \\times h$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$V = 6 \\times B \\times h$<\/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: $V = \\frac{1}{3} \\times B \\times h$<br\/>The formula for the volume of the triangular pyramid is $V = \\frac{1}{3} \\times B \\times h$.<\/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\">Find out the base area of a triangular pyramid whose height is 8 inches and volume is 256 cubic inches.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">16 sq. inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">2,401 sq. inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">96 sq. inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">32 sq. inches<\/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: 96 sq. inches<br\/>Base area of triangular pyramid $= \\frac{V \\times 3}{h} = \\frac{256 \\times 3}{8} = 96$ sq. inches<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Find out the volume of a triangular pyramid whose base area is $36\\; cm^{2}$ and height is 10 cm.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">125 cubic cm<\/div><div class=\"spq_answer_block\" data-value=\"1\">240 cubic cm<\/div><div class=\"spq_answer_block\" data-value=\"2\">254 cubic cm<\/div><div class=\"spq_answer_block\" data-value=\"3\">120 cubic cm<\/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: 120 cubic cm<br\/>Volume of triangular pyramid $= \\frac{1}{3} \\times B \\times h = \\frac{1}{3} \\times 36 \\times 10 = 120$ cubic cm.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What is the volume of a regular triangular pyramid whose edge length of one of the faces is 7 inches?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">30.42 cubic in<\/div><div class=\"spq_answer_block\" data-value=\"1\">60.42 cubic in<\/div><div class=\"spq_answer_block\" data-value=\"2\">50.42 cubic in<\/div><div class=\"spq_answer_block\" data-value=\"3\">40.42 cubic in<\/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: 40.42 cubic in<br\/>Volume of a regular triangular pyramid $= \\frac{a^{3}}{6\\sqrt{2}} = \\frac{7^{3}}{6\\sqrt{2}} = 40.42$ cubic in.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Find out the height of a triangular pyramid whose base area is $120\\; m^{2}$ and volume is $600\\; m^{3}$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">15 m<\/div><div class=\"spq_answer_block\" data-value=\"1\">24 m<\/div><div class=\"spq_answer_block\" data-value=\"2\">25 m<\/div><div class=\"spq_answer_block\" data-value=\"3\">12 m<\/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: 15 m<br\/>Height of a triangular pyramid $= \\frac{V \\times 3}{b} = \\frac{600 \\times 3}{120} = 15$ m.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n     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                             \"text\": \"The formula for the volume of the triangular pyramid is $$V = \\\\frac{1}{3} \\\\times B \\\\times h$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$V = \\\\frac{1}{3} \\\\times B \\\\times h$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The formula for the volume of the triangular pyramid is $$V = \\\\frac{1}{3} \\\\times B \\\\times h$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The formula for the volume of the triangular pyramid is $$V = \\\\frac{1}{3} \\\\times B \\\\times h$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find out the base area of a triangular pyramid whose height is 8 inches and volume is 256 cubic inches.\",\n                    \"text\": \"Find out the base area of a triangular pyramid whose height is 8 inches and volume is 256 cubic inches.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Base area of triangular pyramid $$= \\\\frac{V \\\\times 3}{h} = \\\\frac{256 \\\\times 3}{8} = 96$$ sq. inches\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"16 sq. inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base area of triangular pyramid $$= \\\\frac{V \\\\times 3}{h} = \\\\frac{256 \\\\times 3}{8} = 96$$ sq. inches\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2,401 sq. inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base area of triangular pyramid $$= \\\\frac{V \\\\times 3}{h} = \\\\frac{256 \\\\times 3}{8} = 96$$ sq. inches\"\n          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 \"@type\": \"Comment\",\n                      \"text\": \"Volume of triangular pyramid $$= \\\\frac{1}{3} \\\\times B \\\\times h = \\\\frac{1}{3} \\\\times 36 \\\\times 10 = 120$$ cubic cm.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"125 cubic cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of triangular pyramid $$= \\\\frac{1}{3} \\\\times B \\\\times h = \\\\frac{1}{3} \\\\times 36 \\\\times 10 = 120$$ cubic cm.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"240 cubic cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of triangular pyramid $$= \\\\frac{1}{3} \\\\times B \\\\times h = \\\\frac{1}{3} \\\\times 36 \\\\times 10 = 120$$ cubic cm.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"254 cubic cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of triangular pyramid $$= \\\\frac{1}{3} \\\\times B \\\\times h = \\\\frac{1}{3} \\\\times 36 \\\\times 10 = 120$$ cubic cm.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"120 cubic cm\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Volume of triangular pyramid $$= \\\\frac{1}{3} \\\\times B \\\\times h = \\\\frac{1}{3} \\\\times 36 \\\\times 10 = 120$$ cubic cm.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Volume of triangular pyramid $$= \\\\frac{1}{3} \\\\times B \\\\times h = \\\\frac{1}{3} \\\\times 36 \\\\times 10 = 120$$ cubic cm.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the volume of a regular triangular pyramid whose edge length of one of the faces is 7 inches?\",\n                    \"text\": \"What is the volume of a regular triangular pyramid whose edge length of one of the faces is 7 inches?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Volume of a regular triangular pyramid $$= \\\\frac{a^{3}}{6\\\\sqrt{2}} = \\\\frac{7^{3}}{6\\\\sqrt{2}} = 40.42$$ cubic in.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"30.42 cubic in\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of a regular triangular pyramid $$= \\\\frac{a^{3}}{6\\\\sqrt{2}} = \\\\frac{7^{3}}{6\\\\sqrt{2}} = 40.42$$ cubic in.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"60.42 cubic in\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of a regular triangular pyramid $$= \\\\frac{a^{3}}{6\\\\sqrt{2}} = \\\\frac{7^{3}}{6\\\\sqrt{2}} = 40.42$$ cubic in.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"50.42 cubic in\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of a regular triangular pyramid $$= \\\\frac{a^{3}}{6\\\\sqrt{2}} = \\\\frac{7^{3}}{6\\\\sqrt{2}} = 40.42$$ cubic in.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"40.42 cubic in\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Volume of a regular triangular pyramid $$= \\\\frac{a^{3}}{6\\\\sqrt{2}} = \\\\frac{7^{3}}{6\\\\sqrt{2}} = 40.42$$ cubic in.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Volume of a regular triangular pyramid $$= \\\\frac{a^{3}}{6\\\\sqrt{2}} = \\\\frac{7^{3}}{6\\\\sqrt{2}} = 40.42$$ cubic in.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find out the height of a triangular pyramid whose base area is $$120\\\\; m^{2}$$ and volume is $$600\\\\; m^{3}$$.\",\n                    \"text\": \"Find out the height of a triangular pyramid whose base area is $$120\\\\; m^{2}$$ and volume is $$600\\\\; m^{3}$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Height of a triangular pyramid $$= \\\\frac{V \\\\times 3}{b} = \\\\frac{600 \\\\times 3}{120} = 15$$ m.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"24 m\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Height of a triangular pyramid $$= \\\\frac{V \\\\times 3}{b} = \\\\frac{600 \\\\times 3}{120} = 15$$ m.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"25 m\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Height of a triangular pyramid $$= \\\\frac{V \\\\times 3}{b} = \\\\frac{600 \\\\times 3}{120} = 15$$ m.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12 m\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Height of a triangular pyramid $$= \\\\frac{V \\\\times 3}{b} = \\\\frac{600 \\\\times 3}{120} = 15$$ m.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"15 m\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Height of a triangular pyramid $$= \\\\frac{V \\\\times 3}{b} = \\\\frac{600 \\\\times 3}{120} = 15$$ m.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Height of a triangular pyramid $$= \\\\frac{V \\\\times 3}{b} = \\\\frac{600 \\\\times 3}{120} = 15$$ m.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-frequently-asked-questions-on-the-volume-of-a-triangular-pyramid\">Frequently Asked Questions on the Volume of a Triangular Pyramid<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-3d10248c-cf30-4bb0-95c2-c44739aee173\" 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-0-3d10248c-cf30-4bb0-95c2-c44739aee173\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3d10248c-cf30-4bb0-95c2-c44739aee173\"><strong>Is the volume of a regular triangular pyramid the same as a tetrahedron?<\/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-0-3d10248c-cf30-4bb0-95c2-c44739aee173\">\n\n<p class=\"eplus-wrapper\">Yes, the volume of a regular triangular pyramid is the same as the volume of a tetrahedron.<\/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-1-3d10248c-cf30-4bb0-95c2-c44739aee173\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3d10248c-cf30-4bb0-95c2-c44739aee173\"><strong>What is an oblique triangular pyramid?<\/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-1-3d10248c-cf30-4bb0-95c2-c44739aee173\">\n\n<p class=\"eplus-wrapper\">An oblique triangular pyramid is a non-right pyramid in which the height is not perpendicular to the base.<\/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-2-3d10248c-cf30-4bb0-95c2-c44739aee173\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3d10248c-cf30-4bb0-95c2-c44739aee173\"><strong>What is the surface area of a regular triangular pyramid?<\/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-2-3d10248c-cf30-4bb0-95c2-c44739aee173\">\n\n<p class=\"eplus-wrapper\">The surface area of a regular triangular pyramid is the sum of the area of each of its faces. It is given by the formula, $A = \\sqrt{3}a^{2}$ , where <em>a<\/em> is the side of any of the equilateral triangles in its faces.<\/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-3-3d10248c-cf30-4bb0-95c2-c44739aee173\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3d10248c-cf30-4bb0-95c2-c44739aee173\"><strong>What is the volume of a right triangular pyramid?<\/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-3-3d10248c-cf30-4bb0-95c2-c44739aee173\">\n\n<p class=\"eplus-wrapper\">A right triangular pyramid is a pyramid that has its apex right above its center of the base.The right triangular pyramid volume is given by the formula $V = \\frac{1}{3} \\times B \\times h$, where B is the area of the triangular base and h is the height (the distance from the apex to the base).<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is The Volume of a Triangular Pyramid? Let\u2019s imagine you are making homemade chocolate and want to shape it somewhat like Toblerone. You go to the market and buy a triangular pyramid-shaped setting mold. You will need to work out the volume of the triangular pyramid-shaped mold to find the amount of chocolate you &#8230; <a title=\"Volume of a Triangular Pyramid: Definition, Example, Facts\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-triangular-pyramid\" aria-label=\"More on Volume of a Triangular Pyramid: Definition, Example, Facts\">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-26036","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\/26036","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=26036"}],"version-history":[{"count":13,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26036\/revisions"}],"predecessor-version":[{"id":39919,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26036\/revisions\/39919"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26036"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26036"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26036"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}