A polygon with 9 sides has how many diagonals?<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n The number of diagonals in a polygon with 9 sides is 27.<\/p>\n\n\n\n To calculate the number of diagonals in any polygon, the formula used is: D=n(n\u22123)2D = \\frac{n(n – 3)}{2}<\/p>\n\n\n\n Where:<\/p>\n\n\n\n For a polygon with 9 sides (n = 9), substituting into the formula: D=9(9\u22123)2D = \\frac{9(9 – 3)}{2} D=9\u00d762D = \\frac{9 \\times 6}{2} D=542D = \\frac{54}{2} D=27D = 27<\/p>\n\n\n\n Therefore, a polygon with 9 sides has 27 diagonals.<\/p>\n\n\n\n Explanation:<\/strong> For a 9-sided polygon, the total number of line segments between any two vertices is: (92)=9(8)2=36\\binom{9}{2} = \\frac{9(8)}{2} = 36<\/p>\n\n\n\n However, the 9 sides of the polygon are not diagonals, so we subtract 9 from this total. Thus, the number of diagonals is: 36\u22129=2736 – 9 = 27<\/p>\n\n\n\n This method applies to any polygon. For a polygon with more sides, simply use the formula to calculate the number of diagonals based on the number of sides.<\/p>\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" A polygon with 9 sides has how many diagonals? The correct answer and explanation is: The number of diagonals in a polygon with 9 sides is 27. To calculate the number of diagonals in any polygon, the formula used is: D=n(n\u22123)2D = \\frac{n(n – 3)}{2} Where: For a polygon with 9 sides (n = 9), […]<\/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-240617","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240617","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=240617"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240617\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=240617"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=240617"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=240617"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
A diagonal is a line segment that connects two non-adjacent vertices in a polygon. For any polygon, the total number of line segments that can be drawn between any two vertices is given by the combination formula (n2)\\binom{n}{2}, which calculates the number of ways to choose two vertices from nn vertices. This gives: (n2)=n(n\u22121)2\\binom{n}{2} = \\frac{n(n – 1)}{2}<\/p>\n\n\n\n