{"id":1644,"date":"2022-04-21T09:50:26","date_gmt":"2022-04-21T09:50:26","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1644"},"modified":"2024-01-01T15:32:29","modified_gmt":"2024-01-01T15:32:29","slug":"pentagonal-prism-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/pentagonal-prism","title":{"rendered":"Pentagonal Prism &#8211; Definition with Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><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-95f05acf-5161-4342-a177-ce2c3eade3bb\" 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\/geometry\/pentagonal-prism#0-what-is-a-pentagonal-prism>What is a Pentagonal Prism?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/pentagonal-prism#2-surface-area-of-a-pentagonal-prism>Surface Area of a Pentagonal Prism<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/pentagonal-prism#5-the-volume-of-a-pentagonal-prism->The Volume of a Pentagonal Prism&nbsp;<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/pentagonal-prism#6-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/pentagonal-prism#7-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/pentagonal-prism#8-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us look at the following pictures.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/digital-pentagonal-prism-clock.png\" alt=\"Digital pentagonal prism clock\" class=\"wp-image-37047\" title=\"Digital pentagonal prism clock\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/digital-pentagonal-prism-clock.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/digital-pentagonal-prism-clock-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Can you guess its shape?<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This is shaped like a pentagonal prism. <\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-pentagonal-prism\">What is a Pentagonal Prism?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A pentagonal prism or five-sided polygonal prism is a prism that consists of two pentagonal bases (the top and the bottom) and five rectangular sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Pentagonal Prism is a heptahedron that consists of:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Five rectangular sides<\/li>\n\n\n\n<li class=\"eplus-wrapper\">15 edges<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Ten vertices<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Seven Faces<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It is easier to understand how a usual pentagonal prism looks by going through the image below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"681\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-to-make-a-pentagonal-prism.png\" alt=\"Steps to make a pentagonal prism\" class=\"wp-image-37048\" title=\"Steps to make a pentagonal prism\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-to-make-a-pentagonal-prism.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-to-make-a-pentagonal-prism-273x300.png 273w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this image, we can see that if we draw two pentagons (one on the top and the other on the bottom) and then connect them through straight lines, we will get a pentagonal prism.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">You can find many real-life examples of pentagonal prisms.&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Pentagon &#8211; US Defence Department Headquarter<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"492\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/headquarters-of-the-us-department-of-defense.png\" alt=\"Headquarters of the U.S. Department of Defense\" class=\"wp-image-37050\" title=\"Headquarters of the U.S. Department of Defense\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/headquarters-of-the-us-department-of-defense.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/headquarters-of-the-us-department-of-defense-300x238.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Clocks<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"420\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/analog-pentagonal-clock.png\" alt=\"Analog pentagonal clock\" class=\"wp-image-37051\" title=\"Analog pentagonal clock\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/analog-pentagonal-clock.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/analog-pentagonal-clock-300x203.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Barns<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"535\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pentagonal-barn.png\" alt=\"Pentagonal barn\" class=\"wp-image-37052\" title=\"Pentagonal barn\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pentagonal-barn.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pentagonal-barn-300x259.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Nuts<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"530\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pentagonal-nut.png\" alt=\"Pentagonal nut\" class=\"wp-image-37053\" title=\"Pentagonal nut\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pentagonal-nut.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pentagonal-nut-300x256.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-net-of-a-pentagonal-prism\">Net of a Pentagonal Prism<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/net-of-a-pentagonal-prism.png\" alt=\"Net of a pentagonal prism\" class=\"wp-image-37054\" title=\"Net of a pentagonal prism\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/net-of-a-pentagonal-prism.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/net-of-a-pentagonal-prism-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-surface-area-of-a-pentagonal-prism\">Surface Area of a Pentagonal Prism<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A pentagonal prism has two types of surface areas: total surface area and lateral surface area.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"3-total-surface-area-of-a-pentagonal-prism\">Total Surface Area of a Pentagonal Prism<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A regular pentagonal prism&#8217;s total surface area gives each face&#8217;s area (i.e., seven prism faces). Thus, the total surface area of the regular pentagonal prism is calculated as:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">TSA $= 5ab + 5bh$ square units.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here <em>a<\/em> is the apothem length (a line that connects the center of the regular polygon to the midpoint of one of the sides of the polygon) of the pentagonal base, <em>b<\/em> is the side length of the base, and <em>h<\/em> is the height of a pentagonal prism.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"361\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pentagonal-prism-with-side-apothem-and-height-marked.png\" alt=\"Pentagonal prism with side, apothem, and height marked\" class=\"wp-image-37055\" title=\"Pentagonal prism with side, apothem, and height marked\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pentagonal-prism-with-side-apothem-and-height-marked.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pentagonal-prism-with-side-apothem-and-height-marked-300x175.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-lateral-surface-area-of-a-pentagonal-prism-\">Lateral Surface Area of a Pentagonal Prism&nbsp;<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">One can also calculate the lateral or curved surface area of a regular pentagonal prism using the formula below:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">LSA $= 5bh$, where <em>b<\/em> is the side length of the base, and <em>h<\/em> is the height of the pentagonal prism<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-the-volume-of-a-pentagonal-prism-\">The Volume of a Pentagonal Prism&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The volume of a pentagonal prism represents the space occupied by that prism. So, we can obtain the value of the pentagonal prism using a simple formula.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$V =$ area of base$\\times$height.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">However, to use the above formula, we need to know the area of the base of a pentagonal prism. Thus, to calculate the area of the base of a regular prism, the following formula is applied:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of base $= 1\/2$$ \\times$ perimeter $\\times$ apothem length or $1\/2$$ \\times$$ 5bh$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In other words, the volume of a regular pentagonal prism can also be calculated using the following formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$V = (5\/2)$$\\times a \\times b \\times h$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Q1. The perimeter of a pentagonal prism is 150 inches, and its height is 55 inches. Calculate its lateral surface area.<\/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\">The perimeter of a pentagonal prism is 150 inches (given).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, $P = 150$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The height of a pentagonal prism is 55 inches (given).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, $h = 55$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the lateral Surface area or LSA $= Ph = (150) \\times (55) = 8,250$ sq. inches<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Q2. If the apothem length, base side, and height of a regular pentagonal prism are 5 inches, 8 inches, and 10 inches, respectively. Find the total surface area of the prism.&nbsp;<\/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\">The apothem length of the pentagonal prism is 5 inches (given).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, $a = 5$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The base length of the pentagonal prism is 8 inches (given).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, $b = 8$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The height of the pentagonal prism is 10 inches (given).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, $h = 10$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Plugging the values in the formula for the surface area of a regular pentagonal prism, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;TSA $= 5ab + 5bh$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= (5 \\times 5 \\times 8) + (5 \\times 8 \\times 10)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the total surface area of the prism is 600 cubic inches.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Q3. Find the volume of a chocolate box shaped as a regular pentagonal prism whose apothem<\/strong> <strong>length is 10 cm, base length is 20 cm, and height is 15 cm.<\/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\">To calculate the volume of a regular pentagonal prism, we use the formula below:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$V = 5\/2$$ \\times a \\times b \\times h$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Plugging the values in the formula for the surface area of a regular pentagonal prism, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$V = 5\/2$$ \\times 10 \\times 20 \\times 15 = 7500$ cubic cm<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the volume of the chocolate box is 7500 cubic cm.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Pentagonal Prism - Definition with Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Identify the type of pentagonal prism below:<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/09\/pp1.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">Right Pentagonal Prism<\/div><div class=\"spq_answer_block\" data-value=\"1\"> Square Pentagonal Prism<\/div><div class=\"spq_answer_block\" data-value=\"2\">Oblique Pentagonal Prism<\/div><div class=\"spq_answer_block\" data-value=\"3\">Cubical Pentagonal Prism<\/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: Right Pentagonal Prism<br\/>It is a Right Pentagonal Prism because it has two congruent and parallel pentagonal faces.<\/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\">If the apothem length (radius of the inscribed circle in a regular polygon) of a pentagonal prism is doubled, its total surface area will:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Its surface area will be doubled<\/div><div class=\"spq_answer_block\" data-value=\"1\">Its surface area will decrease<\/div><div class=\"spq_answer_block\" data-value=\"2\">Its surface area will increase<\/div><div class=\"spq_answer_block\" data-value=\"3\">There will be no difference in its surface area<\/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: Its surface area will increase<br\/>In the above formula of the total surface area (TSA) of a regular pentagonal prism, we learned that<br>\r\nTSA $= 5ab + 5bh$. This means that if the apothem length will double, its total surface area<br>\r\nwill increase, but not double.<\/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\">Suppose the base length of a regular pentagonal prism is doubled, what will happen to its lateral surface area?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Its lateral surface area will be doubled<\/div><div class=\"spq_answer_block\" data-value=\"1\">Its lateral surface area will decrease<\/div><div class=\"spq_answer_block\" data-value=\"2\">Its lateral surface area will increase<\/div><div class=\"spq_answer_block\" data-value=\"3\">There will be no difference in its lateral surface area<\/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: Its lateral surface area will be doubled<br\/>We have learned that the lateral surface area of a regular pentagonal prism is $5bh$. So, if the height of the pentagonal prism doubles, we can conclude that its lateral surface area will also be doubled.<\/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\": \"Pentagonal Prism - Definition with Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Pentagonal Prism\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the type of pentagonal prism below:\",\n                    \"text\": \"Identify the type of pentagonal prism below: <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/09\/pp1.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"It is a Right Pentagonal Prism because it has two congruent and parallel pentagonal faces.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \" Square Pentagonal Prism\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It is a Right Pentagonal Prism because it has two congruent and parallel pentagonal faces.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Oblique Pentagonal Prism\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It is a Right Pentagonal Prism because it has two congruent and parallel pentagonal faces.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Cubical Pentagonal Prism\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It is a Right Pentagonal Prism because it has two congruent and parallel pentagonal faces.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Right Pentagonal Prism\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"It is a Right Pentagonal Prism because it has two congruent and parallel pentagonal faces.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"It is a Right Pentagonal Prism because it has two congruent and parallel pentagonal faces.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the apothem length (radius of the inscribed circle in a regular polygon) of a pentagonal prism is doubled, its total surface area will:\",\n                    \"text\": \"If the apothem length (radius of the inscribed circle in a regular polygon) of a pentagonal prism is doubled, its total surface area will:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In the above formula of the total surface area (TSA) of a regular pentagonal prism, we learned that<br>\r\nTSA $$= 5ab + 5bh$$. This means that if the apothem length will double, its total surface area<br>\r\nwill increase, but not double.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Its surface area will be doubled\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the above formula of the total surface area (TSA) of a regular pentagonal prism, we learned that<br>\r\nTSA $$= 5ab + 5bh$$. This means that if the apothem length will double, its total surface area<br>\r\nwill increase, but not double.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Its surface area will decrease\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the above formula of the total surface area (TSA) of a regular pentagonal prism, we learned that<br>\r\nTSA $$= 5ab + 5bh$$. This means that if the apothem length will double, its total surface area<br>\r\nwill increase, but not double.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"There will be no difference in its surface area\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the above formula of the total surface area (TSA) of a regular pentagonal prism, we learned that<br>\r\nTSA $$= 5ab + 5bh$$. This means that if the apothem length will double, its total surface area<br>\r\nwill increase, but not double.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Its surface area will increase\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In the above formula of the total surface area (TSA) of a regular pentagonal prism, we learned that<br>\r\nTSA $$= 5ab + 5bh$$. This means that if the apothem length will double, its total surface area<br>\r\nwill increase, but not double.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In the above formula of the total surface area (TSA) of a regular pentagonal prism, we learned that<br>\r\nTSA $$= 5ab + 5bh$$. This means that if the apothem length will double, its total surface area<br>\r\nwill increase, but not double.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Suppose the base length of a regular pentagonal prism is doubled, what will happen to its lateral surface area?\",\n                    \"text\": \"Suppose the base length of a regular pentagonal prism is doubled, what will happen to its lateral surface area?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We have learned that the lateral surface area of a regular pentagonal prism is $$5bh$$. So, if the height of the pentagonal prism doubles, we can conclude that its lateral surface area will also be doubled.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Its lateral surface area will decrease\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We have learned that the lateral surface area of a regular pentagonal prism is $$5bh$$. So, if the height of the pentagonal prism doubles, we can conclude that its lateral surface area will also be doubled.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Its lateral surface area will increase\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We have learned that the lateral surface area of a regular pentagonal prism is $$5bh$$. So, if the height of the pentagonal prism doubles, we can conclude that its lateral surface area will also be doubled.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"There will be no difference in its lateral surface area\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We have learned that the lateral surface area of a regular pentagonal prism is $$5bh$$. So, if the height of the pentagonal prism doubles, we can conclude that its lateral surface area will also be doubled.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Its lateral surface area will be doubled\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We have learned that the lateral surface area of a regular pentagonal prism is $$5bh$$. So, if the height of the pentagonal prism doubles, we can conclude that its lateral surface area will also be doubled.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We have learned that the lateral surface area of a regular pentagonal prism is $$5bh$$. So, if the height of the pentagonal prism doubles, we can conclude that its lateral surface area will also be doubled.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-41d6f79e-2d43-4b1f-8429-bbd97be9a81c\" 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-0-41d6f79e-2d43-4b1f-8429-bbd97be9a81c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-41d6f79e-2d43-4b1f-8429-bbd97be9a81c\"><strong>What is a prism?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-41d6f79e-2d43-4b1f-8429-bbd97be9a81c\">\n\n<p class=\"wp-block-paragraph\"> Any 3-D shape which has two parallel and congruent faces or bases is defined as a prism.<\/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-1-41d6f79e-2d43-4b1f-8429-bbd97be9a81c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-41d6f79e-2d43-4b1f-8429-bbd97be9a81c\"><strong>What do face and base mean in 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-1-41d6f79e-2d43-4b1f-8429-bbd97be9a81c\">\n\n<p class=\"wp-block-paragraph\">The faces of a pentagonal prism are the flat side of a 3-D object, whereas its base is defined as one of the two congruent sides of the prism.<\/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-2-41d6f79e-2d43-4b1f-8429-bbd97be9a81c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-41d6f79e-2d43-4b1f-8429-bbd97be9a81c\"><strong>What do you mean by 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-2-41d6f79e-2d43-4b1f-8429-bbd97be9a81c\">\n\n<p class=\"wp-block-paragraph\">Apothem length of a regular polygon is the line that connects the center of the regular polygon to the midpoint of one of the sides of the polygon. It is also used to find any regular polygon&#8217;s surface area and volume, including a pentagonal prism.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"321\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/09\/pentagonal-prism-faq.png\" alt=\"Apothem length of regular polygons\" class=\"wp-image-10683\" title=\"Apothem length of regular polygons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/09\/pentagonal-prism-faq.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/09\/pentagonal-prism-faq-300x155.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Let us look at the following pictures. Can you guess its shape? This is shaped like a pentagonal prism. What is a Pentagonal Prism? A pentagonal prism or five-sided polygonal prism is a prism that consists of two pentagonal bases (the top and the bottom) and five rectangular sides. Pentagonal Prism is a heptahedron that &#8230; <a title=\"Pentagonal Prism &#8211; Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/pentagonal-prism\" aria-label=\"More on Pentagonal Prism &#8211; Definition with Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1644","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\/1644","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=1644"}],"version-history":[{"count":20,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1644\/revisions"}],"predecessor-version":[{"id":37056,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1644\/revisions\/37056"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1644"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1644"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1644"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}