{"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 wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\">$V = \\frac{1}{3} \\times B \\times h$ cubic units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">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 wp-block-paragraph\"><strong>Note:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula for a regular triangular pyramid volume is:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$V = \\frac{a^{3}}{6\\sqrt{2}}$ cubic units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\">$V = \\frac{1}{3} \\times Area of base \\times h$<\/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 wp-block-paragraph\">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 wp-block-paragraph\">$A = \\frac{1}{2} \\times b \\times h$&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\">$V = \\frac{a^{3}}{6\\sqrt{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\"><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 wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">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 wp-block-paragraph\">We know Volume $= \\frac{1}{3} \\times B \\times h$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substituting the values we get,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Volume = \\frac{1}{3} \\times 19 \\times 1.5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Volume = 19 \\times 0.5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Volume = 9.5\\; cubic\\; inches$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><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 wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It is given that B $= 175$ and V $= 1050$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Volume of a triangular pyramid $= \\frac{1}{3} \\times B \\times h$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$1050 = \\frac{1}{3} \\times 175 \\times h$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Rearranging the values we get,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$h = \\frac{3 \\times 1050}{175}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$h = 18\\; units$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, the height of the pyramid is 18 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><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 wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">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 wp-block-paragraph\">We know that the volume of a regular triangular pyramid is&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$V = \\frac{a^{3}}{6\\sqrt{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substituting \u201c<em>a<\/em>\u201d as $9\\sqrt{2}$ we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$V = \\frac{(9\\sqrt{2})^{3}}{6\\sqrt{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$V = \\frac{9\\sqrt{2}&nbsp;\\times 9\\sqrt{2} \\times 9\\sqrt{2}}{6\\sqrt{2}} = 243$ cubic units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, the volume of the regular triangular pyramid is 243 cubic units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><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 wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">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 wp-block-paragraph\">We know that the volume of a regular triangular pyramid is:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$V = \\frac{a^{3}}{6\\sqrt{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substituting <em>\u201cV<\/em>\u201d as $18\\sqrt{2}$ we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$18\\sqrt{2} = \\frac{(a)^{3}}{6\\sqrt{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a^{3} = 18\\sqrt{2} \\times 6\\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a^{3} = 216$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Taking a cube root on both sides, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a = 6$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, the height of the regular triangular pyramid is 6 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><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 wp-block-paragraph\"><strong>Solution:&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">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 wp-block-paragraph\">It is given that $V_{1} = 50$ and $V_{2} = 75$ .<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know, Volume$= \\frac{1}{3} \\times B \\times h$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\">$\\frac{V_{2}}{V_{1}} = \\frac{^{\\frac{1}{3} \\times B \\times h_{2}}}{^{\\frac{1}{3} \\times B \\times h_{1}}} = \\frac{75}{50}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{h_{2}}{h_{1}} = \\frac{3}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiplying both sides by 100.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{h_{2}}{h_{1}} \\times 100 = \\frac{3}{2} \\times 100$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{h2}{h1} \\times 100 = 1.5 \\times 100 = 150\\%$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">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 wp-block-paragraph\"><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        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Volume of a Triangular Pyramid: Definition, Example, Facts\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Volume of a Triangular Pyramid\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    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the volume of the triangular pyramid is $$V = \\\\frac{1}{3} \\\\times B \\\\times h$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$V = 3 \\\\times B \\\\times h$$\",\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                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$V = 6 \\\\times B \\\\times h$$\",\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                                }],\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\": 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                                 \"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\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"32 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                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"96 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                      \"answerExplanation\": {\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\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find out the volume of a triangular pyramid whose base area is $$36\\\\; cm^{2}$$ and height is 10 cm.\",\n                    \"text\": \"Find out the volume of a triangular pyramid whose base area is $$36\\\\; cm^{2}$$ and height is 10 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                    \"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 wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\">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 wp-block-paragraph\">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}]}}