{"id":26234,"date":"2025-06-19T11:23:28","date_gmt":"2025-06-19T11:23:28","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=26234"},"modified":"2025-06-19T11:23:31","modified_gmt":"2025-06-19T11:23:31","slug":"consider-a-pyramid-whose-base-is-a-regular-n-gonaethat-is-a-regular-polygon-with-n-sides","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/consider-a-pyramid-whose-base-is-a-regular-n-gonaethat-is-a-regular-polygon-with-n-sides\/","title":{"rendered":"Consider a pyramid whose base is a regular n-gon\u00e2\u20ac\u201dthat is, a regular polygon with n sides."},"content":{"rendered":"\n<p>Consider a pyramid whose base is a regular n-gon\u00e2\u20ac\u201dthat is, a regular polygon with n sides. How many vertices would such a pyramid have? How many faces? How many edges? (a) Describe the relationship between the number of vertices of an n-gon prism and of an n-gon pyramid. (Select one) An n-gon prism has n + 1 more vertices than an n-gon pyramid. An n-gon prism has n \u00e2\u02c6\u2019 2 more vertices than an n-gon pyramid. An n-gon prism has n more vertices than an n-gon pyramid. An n-gon prism has n \u00e2\u02c6\u2019 1 more vertices than an n-gon pyramid. An n-gon prism has n + 2 more vertices than an n-gon pyramid. (b) Describe the relationship between the number of faces of an n-gon prism and of an n-gon pyramid. (Select one) An n-gon prism has one more face than an n-gon pyramid. An n-gon prism has two fewer faces than an n-gon pyramid. An n-gon prism has two more faces than an n-gon pyramid. An n-gon prism has one less face than an n-gon pyramid. An n-gon prism has the same number of faces as an n-gon pyramid. (c) Describe the relationship between the number of edges of an n-gon prism and of an n-gon pyramid. (Select one) An n-gon prism has n \u00e2\u02c6\u2019 1 more edges than an n-gon pyramid. An n-gon prism has n \u00e2\u02c6\u2019 2 more edges than an n-gon pyramid. An n-gon prism has n more edges than an n-gon pyramid. An n-gon prism has n + 2 more edges than an n-gon pyramid. An n-gon prism has n + 1 more edges than an n-gon pyramid<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we need to understand the properties of an <strong>n-gon pyramid<\/strong> and an <strong>n-gon prism<\/strong>. Let&#8217;s break it down carefully:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>n-gon Pyramid<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A pyramid with a regular <em>n<\/em>-gon base has:\n<ul class=\"wp-block-list\">\n<li><strong>Vertices:<\/strong> nnn base vertices plus 1 apex = n+1n + 1n+1 vertices<\/li>\n\n\n\n<li><strong>Faces:<\/strong> nnn triangular lateral faces plus 1 base = n+1n + 1n+1 faces<\/li>\n\n\n\n<li><strong>Edges:<\/strong> nnn base edges plus nnn edges from the apex to each base vertex = 2n2n2n edges<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>n-gon Prism<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A prism has two congruent n-gon bases and vertical edges connecting corresponding vertices:\n<ul class=\"wp-block-list\">\n<li><strong>Vertices:<\/strong> 2n2n2n (n from top base and n from bottom base)<\/li>\n\n\n\n<li><strong>Faces:<\/strong> nnn rectangular lateral faces plus 2 n-gon bases = n+2n + 2n+2 faces<\/li>\n\n\n\n<li><strong>Edges:<\/strong> nnn top base edges + nnn bottom base edges + nnn vertical edges = 3n3n3n edges<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(a) <strong>Relationship Between Vertices<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Pyramid: n+1n + 1n+1 vertices<\/li>\n\n\n\n<li>Prism: 2n2n2n vertices<\/li>\n\n\n\n<li>Difference: 2n\u2212(n+1)=n\u221212n &#8211; (n + 1) = n &#8211; 12n\u2212(n+1)=n\u22121<br>\u2705 <strong>Correct answer:<\/strong> <strong>An n-gon prism has n \u2212 1 more vertices than an n-gon pyramid.<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(b) <strong>Relationship Between Faces<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Pyramid: n+1n + 1n+1 faces<\/li>\n\n\n\n<li>Prism: n+2n + 2n+2 faces<\/li>\n\n\n\n<li>Difference: (n+2)\u2212(n+1)=1(n + 2) &#8211; (n + 1) = 1(n+2)\u2212(n+1)=1<br>\u2705 <strong>Correct answer:<\/strong> <strong>An n-gon prism has one more face than an n-gon pyramid.<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(c) <strong>Relationship Between Edges<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Pyramid: 2n2n2n edges<\/li>\n\n\n\n<li>Prism: 3n3n3n edges<\/li>\n\n\n\n<li>Difference: 3n\u22122n=n3n &#8211; 2n = n3n\u22122n=n<br>\u2705 <strong>Correct answer:<\/strong> <strong>An n-gon prism has n more edges than an n-gon pyramid.<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(a):<\/strong> An n-gon prism has <strong>n \u2212 1 more vertices<\/strong> than an n-gon pyramid.<\/li>\n\n\n\n<li><strong>(b):<\/strong> An n-gon prism has <strong>one more face<\/strong> than an n-gon pyramid.<\/li>\n\n\n\n<li><strong>(c):<\/strong> An n-gon prism has <strong>n more edges<\/strong> than an n-gon pyramid.<\/li>\n<\/ul>\n\n\n\n<p>These relationships hold true for any polygon with n sides and illustrate how adding a second base (as in a prism) changes the geometric structure.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-76.jpeg\" alt=\"\" class=\"wp-image-26235\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-76.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-76-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Consider a pyramid whose base is a regular n-gon\u00e2\u20ac\u201dthat is, a regular polygon with n sides. How many vertices would such a pyramid have? How many faces? How many edges? (a) Describe the relationship between the number of vertices of an n-gon prism and of an n-gon pyramid. (Select one) An n-gon prism has n [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-26234","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26234","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=26234"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26234\/revisions"}],"predecessor-version":[{"id":26236,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26234\/revisions\/26236"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}