{"id":31949,"date":"2023-07-16T21:30:00","date_gmt":"2023-07-16T21:30:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=31949"},"modified":"2023-07-17T10:14:01","modified_gmt":"2023-07-17T10:14:01","slug":"volume-of-a-pentagonal-prism-definition-formula-examples-facts","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-pentagonal-prism","title":{"rendered":"Volume of a Pentagonal Prism &#8211; Definition, Formula, Examples, 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-83eec43d-d34e-43c3-92b6-d0b58973e8bc\" 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-pentagonal-prism#0-what-is-the-volume-of-a-pentagonal-prism>What Is the Volume of a Pentagonal Prism?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-pentagonal-prism#1-volume-of-a-pentagonal-prism-formula>Volume of a Pentagonal Prism Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-pentagonal-prism#2-how-to-find-the-volume-of-a-pentagonal-prism>How to Find the Volume of a Pentagonal Prism<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-pentagonal-prism#5-solved-examples-on-volume-of-a-pentagonal-prism>Solved Examples on Volume of a Pentagonal Prism<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-pentagonal-prism#6-practice-problems-on-volume-of-a-pentagonal-prism>Practice Problems on Volume of a Pentagonal Prism<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-pentagonal-prism#7-frequently-asked-questions-on-volume-of-a-pentagonal-prism>Frequently Asked Questions on Volume of a Pentagonal Prism<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-volume-of-a-pentagonal-prism\">What Is the Volume of a Pentagonal Prism?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The volume of a pentagonal prism is the amount of space occupied by it. It is calculated by the formula: Base <\/strong>$\\times$<strong> area Height. <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/volume\"><strong>Volume<\/strong><\/a><strong> is measured in cubic units such as <\/strong>$inch^{3}$<strong>, <\/strong>$ft^{3}$<strong>, etc.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/pentagonal-prism\">pentagonal prism<\/a> is a three-dimensional solid with two bases (top and bottom) that are pentagons. A pentagonal prism has sides (lateral faces) that are rectangular. Volume of a pentagonal prism is defined as the space occupied within the boundaries of the prism in three-dimensional space.<\/p>\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\" id=\"1-volume-of-a-pentagonal-prism-formula\">Volume of a Pentagonal Prism Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The volume of a prism is calculated by multiplying the area of the base by the height of the prism.<\/p>\n\n\n\n<figure class=\"wp-block-table wj-custom-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Volume of a pentagonal prism $=$ Base area $\\times$ Height<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">$V = \\frac{5}{2} \\times a \\times b \\times h$<br>where,<br>$a =$ length of apothem of the pentagonal base<br>$b =$ base edge (length of sides) of the pentagonal prism<br>$h =$ the height of the pentagonal prism<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Here, we use the following formulas:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Base Area of Pentagonal Prism $=$ Area of a Pentagon&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Base Area $= (12 \\times \\text{Perimeter}) \\times \\text{Apothem}$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Perimeter of a Regular Pentagon $= P = 5 \\times b$&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">where b is the side length<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"451\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/volume-of-pentagonal-prism-formula.png\" alt=\"Volume of pentagonal prism formula\" class=\"wp-image-31958\" title=\"Volume of pentagonal prism formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/volume-of-pentagonal-prism-formula.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/volume-of-pentagonal-prism-formula-300x218.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Keep in mind:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The apothem is the line segment joining the midpoint of one of the sides and the center of the polygon.&nbsp;<\/li>\n\n\n\n<li>Perimeter of a pentagon is equal to the sum of all its sides.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-how-to-find-the-volume-of-a-pentagonal-prism\">How to Find the Volume of a Pentagonal Prism<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When the base-edge (b), height of the prism (h), and apothem of the base (a) is known, we use the following steps to calculate the volume.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1:<\/strong> Find the base area of the given pentagonal prism.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base area $=$ Area of pentagon&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base area $= (\\frac{1}{2} \\times \\text{Perimeter}) \\times \\text{Apothem}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base area $= (\\frac{1}{2} \\times 5b) \\times a$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Perimeter of a regular pentagon $= 5b$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2: <\/strong>Calculate the required volume using the formula:<strong>&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Volume of a pentagonal prism $= \\frac{1}{2} \\times a \\times 5b \\times h$<strong> cubic units.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Volume of a pentagonal prism $= \\frac{5}{2}\\;abh$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$a =$&nbsp; apothem length of the pentagonal prism.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$b =$&nbsp; the base length of the pentagonal prism.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$h =$&nbsp; the pentagonal prism&#8217;s height.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: Find the volume of a pentagonal prism with base-edge <\/strong>$= 7$<strong> units, apothem <\/strong>$(a) \u2248 4.8$<strong> units, height of the prism (h) <\/strong>$= 10$<strong> units.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$a = 4.8$ units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$b = 7$ units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$h = 10$ units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$V = \\frac{5}{2}abh = \\frac{5}{2} \\times 7 \\times 4.8 \\times 10 = 840$ cubic units<strong>&nbsp;<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-facts-about-volume-of-a-pentagonal-prism\">Facts about Volume of a Pentagonal Prism<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>A prism with five rectangular lateral faces (sides) and two pentagonal bases (top and bottom) is called a pentagonal prism.<\/li>\n\n\n\n<li>A pentagonal prism is a kind of heptahedron that has 15 edges, 10 vertices, and 7 faces.<\/li>\n\n\n\n<li>A pentagonal prism has a pentagonal cross-section.<\/li>\n\n\n\n<li>In the right pentagonal prism, the bases are aligned exactly on top of each other.<\/li>\n\n\n\n<li>When the base-edge (b) and and the height of a right regular pentagonal prism (h) is known, we can use the volume formula $V =&nbsp;\\frac{1}{4}\\sqrt{5(5 + 2\\sqrt{5})}b^{2} h \u2248 1.72 b^{2} h$<br><strong>Example:<\/strong> Find the volume of a pentagonal prism with base-edge $= 7$ units and height $= 10$ units. $V = \\frac{1}{4}\\sqrt{5(5 + 2\\sqrt{5})} b^{2} h \u2248 1.72 b^{2} h \u2248 842.8$ cubic units<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we have discussed the volume of a pentagonal prism and the formula for the same. Now let\u2019s look at some solved examples and do some practice problems to understand the concept better.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-solved-examples-on-volume-of-a-pentagonal-prism\">Solved Examples on Volume of a Pentagonal Prism<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Find the volume of a pentagonal prism whose apothem length of 3 inches, base length of 12 inches, and height of 15 inches.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Apothem length (a) $= 3$ inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base length $(b) = 12$ inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Height $(h) = 15$ inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Volume of the pentagonal prism $= \\frac{5}{2} \\times a \\times b \\times h$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{5}{2} \\times 3 \\times 12 \\times 15$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;$= 1350\\; inch^{3}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, the volume of a pentagonal prism $= 1350\\; inch^{3}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Find the apothem length of the pentagonal prism if the height is 20 feet, the base length is 7 feet, and its volume is <\/strong>$1680\\; ft^{3}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Volume of pentagonal prism $= 1240\\; ft^{3}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$h = 20$ feet<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$b = 7$ feet<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Volume of pentagonal prism $= \\frac{5}{2} \\times a \\times b \\times h$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\Rightarrow 1680 = \\frac{5}{2} \\times a \\times 7 \\times 20$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\Rightarrow a = \\frac{2 \\times 1680}{5 \\times 7 \\times 20} = 4.8$ feet<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, apothem length of the pentagonal prism $= 4.8$ feet<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. If the volume of a pentagonal prism is <\/strong>$528\\; ft^{3}$<strong> and the base area is <\/strong>$24\\; ft^{2}$<strong>, then find the height of the prism.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Volume $=&nbsp;528$ cubic feet and base area $= 24$ square feet<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Volume of prism $= base area  \\times height$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp; $\\Rightarrow 528 =24 \\times height$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">  $ \\Rightarrow height = \\frac{528}{24} = 22\\; ft$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, the height of the prism $= 22\\; ft$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. Find the base area of a pentagonal prism if apothem length of 3.4 units and its perimeter is 25 units.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Apothem length $(a) = 3.4$ units, and perimeter $(P) = 28$ units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base area of a pentagonal prism $= \\frac{1}{2} \\times P \\times a$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$= \\frac{1}{2} \\times 25 \\times 3.4$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$= 42.5$ square units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, the base area of a pentagonal prism $= 42.5$ square units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>5. Find the height of the pentagonal prism if the apothem length is 4 inches, the base length is 6 inches and its volume is 540 cubic inches.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">apothem length $(a) = 4$ inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">base-edge $= 6$ inches&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Volume $= 540$ cubic inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Volume of the pentagonal prism $= \\frac{5}{2} \\times a \\times b \\times h$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\Rightarrow 540 = \\frac{5}{2} \\times 4 \\times 6 \\times h$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\Rightarrow 540 = 60\\; h$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\Rightarrow h = \\frac{540}{60}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\Rightarrow h = 9$ inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, the height of a pentagonal prism $= 9$ inches<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-practice-problems-on-volume-of-a-pentagonal-prism\">Practice Problems on Volume of a Pentagonal Prism<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Volume of a Pentagonal Prism - Definition, Formula, Examples, Facts<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Volume of a pentagonal prism is given by<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\text{apothem} \\times \\text{height}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\text{base perimeter} \\times  \\text{height}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\text{base area} \\times \\text{height}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\text{Total surface area} \\times \\text{height}$<\/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: $\\text{base area} \\times \\text{height}$<br\/>Volume of a pentagonal prism $= \\text{base area} \\times \\text{height}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The volume of a pentagonal prism with base-edge b, apothem a, and height h is _________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{2} \\times a \\times b \\times h$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{5}{2} \\times a \\times b \\times h$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{2}{5} \\times a \\times b \\times h$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{5}{2} \\times a \\times h$<\/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: $\\frac{5}{2} \\times a \\times b \\times h$<br\/>Volume of the pentagonal prism $= \\frac{5}{2} \\times a \\times b \\times h$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The volume of a pentagonal prism whose base area is $50\\; ft^{2}$ and height is 5 ft.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$250\\; ft^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$299\\; ft^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$235\\; ft^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$280\\; ft^{3}$<\/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: $250\\; ft^{3}$<br\/>Volume of pentagonal prism $=base area \\times height  = 50 \\times 5 = 250\\; ft^{3}$<\/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\">The base area of a pentagonal prism of apothem length is 2 feet and its perimeter is 15 feet is _____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$38\\; ft^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$30\\; ft^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$55\\; ft^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$15\\; ft^{2}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $15\\; ft^{2}$<br\/>Base area of a pentagonal prism $= \\frac{1}{2} \\times perimeter \\times apothem length$<br>\r\n$\\Rightarrow$ Base area of a pentagonal prism $= \\frac{1}{2} \\times 15 \\times 2 = 15\\; ft^{2}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The volume of a pentagonal prism is ______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">The region covered by all its surfaces<\/div><div class=\"spq_answer_block\" data-value=\"1\">Total area of the lateral faces<\/div><div class=\"spq_answer_block\" data-value=\"2\">Total space occupied by it<\/div><div class=\"spq_answer_block\" data-value=\"3\">Total area of the base<\/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: Total area of the lateral faces<br\/>Volume of the pentagonal prism is the total space occupied by it.<\/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 Pentagonal Prism - Definition, Formula, 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\"text\/html\",\n                                \"text\": \"$$\\\\frac{2}{5} \\\\times a \\\\times b \\\\times h$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of the pentagonal prism $$= \\\\frac{5}{2} \\\\times a \\\\times b \\\\times h$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{5}{2} \\\\times a \\\\times h$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of the pentagonal prism $$= \\\\frac{5}{2} \\\\times a \\\\times b \\\\times h$$\"\n                                    }\n   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\"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The volume of a pentagonal prism whose base area is $$50\\\\; ft^{2}$$ and height is 5 ft.\",\n                    \"text\": \"The volume of a pentagonal prism whose base area is $$50\\\\; ft^{2}$$ and height is 5 ft.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Volume of pentagonal prism $$=base area \\\\times height  = 50 \\\\times 5 = 250\\\\; ft^{3}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$299\\\\; ft^{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of pentagonal prism $$=base area \\\\times height  = 50 \\\\times 5 = 250\\\\; ft^{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$235\\\\; ft^{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of pentagonal prism $$=base area \\\\times height  = 50 \\\\times 5 = 250\\\\; ft^{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$280\\\\; ft^{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of pentagonal prism $$=base area \\\\times height  = 50 \\\\times 5 = 250\\\\; ft^{3}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$250\\\\; ft^{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Volume of pentagonal prism $$=base area \\\\times height  = 50 \\\\times 5 = 250\\\\; ft^{3}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Volume of pentagonal prism $$=base area \\\\times height  = 50 \\\\times 5 = 250\\\\; ft^{3}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The base area of a pentagonal prism of apothem length is 2 feet and its perimeter is 15 feet is _____.\",\n                    \"text\": \"The base area of a pentagonal prism of apothem length is 2 feet and its perimeter is 15 feet is _____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times perimeter \\\\times apothem length$$<br>\r\n$$\\\\Rightarrow$$ Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times 15 \\\\times 2 = 15\\\\; ft^{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$38\\\\; ft^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times perimeter \\\\times apothem length$$<br>\r\n$$\\\\Rightarrow$$ Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times 15 \\\\times 2 = 15\\\\; ft^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$30\\\\; ft^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times perimeter \\\\times apothem length$$<br>\r\n$$\\\\Rightarrow$$ Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times 15 \\\\times 2 = 15\\\\; ft^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$55\\\\; ft^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times perimeter \\\\times apothem length$$<br>\r\n$$\\\\Rightarrow$$ Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times 15 \\\\times 2 = 15\\\\; ft^{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$15\\\\; ft^{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times perimeter \\\\times apothem length$$<br>\r\n$$\\\\Rightarrow$$ Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times 15 \\\\times 2 = 15\\\\; ft^{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times perimeter \\\\times apothem length$$<br>\r\n$$\\\\Rightarrow$$ Base area of a pentagonal prism $$= \\\\frac{1}{2} \\\\times 15 \\\\times 2 = 15\\\\; ft^{2}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The volume of a pentagonal prism is ______.\",\n                    \"text\": \"The volume of a pentagonal prism is ______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Volume of the pentagonal prism is the total space occupied by it.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"The region covered by all its surfaces\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of the pentagonal prism is the total space occupied by it.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Total space occupied by it\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of the pentagonal prism is the total space occupied by it.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Total area of the base\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of the pentagonal prism is the total space occupied by it.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Total area of the lateral faces\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Volume of the pentagonal prism is the total space occupied by it.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Volume of the pentagonal prism is the total space occupied by it.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-frequently-asked-questions-on-volume-of-a-pentagonal-prism\">Frequently Asked Questions on Volume of a Pentagonal Prism<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-566d7d1f-a9de-4b61-8d17-2a053385d4cd\" 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-0-566d7d1f-a9de-4b61-8d17-2a053385d4cd\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-566d7d1f-a9de-4b61-8d17-2a053385d4cd\"><strong>What is a pentagonal prism?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-566d7d1f-a9de-4b61-8d17-2a053385d4cd\">\n\n<p class=\"wp-block-paragraph\">A pentagonal prism is a three-dimensional solid with five rectangular lateral faces and two pentagonal bases (top and bottom).<\/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-1-566d7d1f-a9de-4b61-8d17-2a053385d4cd\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-566d7d1f-a9de-4b61-8d17-2a053385d4cd\"><strong>What is the formula for the surface area of a pentagonal prism?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-566d7d1f-a9de-4b61-8d17-2a053385d4cd\">\n\n<p class=\"wp-block-paragraph\">Surface area of pentagonal prism $= 5ab + 5bh$ square units<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-566d7d1f-a9de-4b61-8d17-2a053385d4cd\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-566d7d1f-a9de-4b61-8d17-2a053385d4cd\"><strong>What is an oblique pentagonal prism?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-566d7d1f-a9de-4b61-8d17-2a053385d4cd\">\n\n<p class=\"wp-block-paragraph\">An oblique prism is one whose sides don&#8217;t meet the base at a right angle.<\/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-3-566d7d1f-a9de-4b61-8d17-2a053385d4cd\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-566d7d1f-a9de-4b61-8d17-2a053385d4cd\"><strong>What is the apothem length of a polygon?<\/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-3-566d7d1f-a9de-4b61-8d17-2a053385d4cd\">\n\n<p class=\"wp-block-paragraph\">Apothem is the line segment that joins any side&#8217;s midpoint and the center of a polygon is called the apothem length. It makes a right angle at the point of intersection with the side.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Volume of a Pentagonal Prism? The volume of a pentagonal prism is the amount of space occupied by it. It is calculated by the formula: Base $\\times$ area Height. Volume is measured in cubic units such as $inch^{3}$, $ft^{3}$, etc. A pentagonal prism is a three-dimensional solid with two bases (top and &#8230; <a title=\"Volume of a Pentagonal Prism &#8211; Definition, Formula, Examples, Facts\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-pentagonal-prism\" aria-label=\"More on Volume of a Pentagonal Prism &#8211; Definition, Formula, Examples, 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-31949","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\/31949","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=31949"}],"version-history":[{"count":14,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31949\/revisions"}],"predecessor-version":[{"id":31970,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31949\/revisions\/31970"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=31949"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=31949"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=31949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}