{"id":245938,"date":"2025-07-06T15:09:20","date_gmt":"2025-07-06T15:09:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245938"},"modified":"2025-07-06T15:09:22","modified_gmt":"2025-07-06T15:09:22","slug":"how-many-faces-edges-and-vertices-does-a-pentagonal-prism-have-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/how-many-faces-edges-and-vertices-does-a-pentagonal-prism-have-2\/","title":{"rendered":"How many faces, edges, and vertices does a pentagonal prism have"},"content":{"rendered":"\n
How many faces, edges, and vertices does a pentagonal prism have? b) How many faces, edges, and vertices does a 100-gonal prism have? c) How many faces, edges, and vertices does an n-gonal prism have?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Let’s go through each part step by step.<\/p>\n\n\n\n
a) Pentagonal Prism:<\/strong><\/h3>\n\n\n\n
A pentagonal prism<\/strong> is a 3D shape formed by joining two pentagonal faces and connecting them with rectangular faces.<\/p>\n\n\n\n
\n
Faces:<\/strong> A pentagonal prism has 7 faces. There are 2 pentagonal faces (one at the top and one at the bottom) and 5 rectangular faces connecting the sides of the pentagons.<\/li>\n\n\n\n
Edges:<\/strong> It has 15 edges. Each pentagonal face has 5 edges, and there are 5 edges connecting the corresponding vertices of the two pentagons (the vertical edges). So the total number of edges is 5+5+5=155 + 5 + 5 = 155+5+5=15.<\/li>\n\n\n\n
Vertices:<\/strong> A pentagonal prism has 10 vertices. Each pentagon has 5 vertices, and since there are two pentagons, the total number of vertices is 5\u00d72=105 \\times 2 = 105\u00d72=10.<\/li>\n<\/ul>\n\n\n\n
b) 100-gonal Prism:<\/strong><\/h3>\n\n\n\n
A 100-gonal prism<\/strong> is a 3D shape with 100 sides in the base, where the base is a 100-sided polygon.<\/p>\n\n\n\n
\n
Faces:<\/strong> It has 102 faces. There are 2 polygonal faces (one at the top and one at the bottom), and 100 rectangular faces connecting the corresponding edges of the two 100-gons.<\/li>\n\n\n\n
Edges:<\/strong> A 100-gonal prism has 300 edges. Each 100-gon has 100 edges, and there are 100 edges connecting the corresponding vertices between the two 100-gons. The total number of edges is 100+100+100=300100 + 100 + 100 = 300100+100+100=300.<\/li>\n\n\n\n
Vertices:<\/strong> It has 200 vertices. Each 100-gon has 100 vertices, and there are two 100-gons, so the total number of vertices is 100\u00d72=200100 \\times 2 = 200100\u00d72=200.<\/li>\n<\/ul>\n\n\n\n
c) n-gonal Prism:<\/strong><\/h3>\n\n\n\n
An n-gonal prism<\/strong> is a 3D shape with an n-sided polygon as the base.<\/p>\n\n\n\n
\n
Faces:<\/strong> An n-gonal prism has n+2n + 2n+2 faces. There are 2 polygonal faces (the top and bottom) and nnn rectangular faces connecting the corresponding edges of the two n-gons.<\/li>\n\n\n\n
Edges:<\/strong> The total number of edges in an n-gonal prism is 3n3n3n. Each n-gon has n edges, and there are n edges connecting the corresponding vertices of the two n-gons, so the total number of edges is n+n+n=3nn + n + n = 3nn+n+n=3n.<\/li>\n\n\n\n
Vertices:<\/strong> The number of vertices in an n-gonal prism is 2n2n2n. Each n-gon has n vertices, and there are two n-gons, so the total number of vertices is n\u00d72=2nn \\times 2 = 2nn\u00d72=2n.<\/li>\n<\/ul>\n\n\n\n
This pattern holds for any n-gonal prism, where the number of faces, edges, and vertices depends on the number of sides (n) of the polygon forming the base.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
How many faces, edges, and vertices does a pentagonal prism have? b) How many faces, edges, and vertices does a 100-gonal prism have? c) How many faces, edges, and vertices does an n-gonal prism have? The Correct Answer and Explanation is: Let’s go through each part step by step. a) Pentagonal Prism: A pentagonal prism […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-245938","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245938","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=245938"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245938\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245938"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245938"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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