{"id":620976,"date":"2023-06-20T18:34:35","date_gmt":"2023-06-20T13:04:35","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=620976"},"modified":"2025-06-11T16:33:09","modified_gmt":"2025-06-11T11:03:09","slug":"polygon-formula","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/","title":{"rendered":"Polygon Formula\u00a0"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#What_is_Polygon\" title=\"What is Polygon?  \">What is Polygon?  <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#What_are_the_types_of_polygons\" title=\"What are the types of polygons? \">What are the types of polygons? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#What_are_convex_and_concave_polygons\" title=\"What are convex and concave polygons? \">What are convex and concave polygons? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#What_are_Regular_and_Irregular_polygons\" title=\"What are Regular and Irregular polygons? \">What are Regular and Irregular polygons? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#Polygon_Formula\" title=\"Polygon Formula: \">Polygon Formula: <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#um_of_angles_of_a_pentagon\" title=\"um of angles of a pentagon \">um of angles of a pentagon <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#Solved_Examples_on_Polygon_Formula\" title=\"Solved Examples on Polygon Formula: \">Solved Examples on Polygon Formula: <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#Frequently_Asked_Questions_on_Polygon_Formula\" title=\"Frequently Asked Questions on Polygon Formula: \">Frequently Asked Questions on Polygon Formula: <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#Polygon_Formula_FAQs\" title=\"Polygon Formula FAQs\">Polygon Formula FAQs<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#How_do_you_find_the_sides_of_a_polygon\" title=\"How do you find the sides of a polygon?\">How do you find the sides of a polygon?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#How_do_you_solve_a_polygon_formula\" title=\"How do you solve a polygon formula?\">How do you solve a polygon formula?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#What_is_polygon_in_math_7\" title=\"What is polygon in math 7? \">What is polygon in math 7? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#What_is_the_formula_for_the_area_of_a_polygon_with_n_sides\" title=\"What is the formula for the area of a polygon with n sides?\">What is the formula for the area of a polygon with n sides?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#What_is_the_area_of_a_polygon_with_5_sides\" title=\"What is the area of a polygon with 5 sides? \">What is the area of a polygon with 5 sides? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#What_is_the_formula_for_regular_polygon\" title=\"What is the formula for regular polygon?\">What is the formula for regular polygon?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#Which_polygon_has_diagonals\" title=\"Which polygon has diagonals? \">Which polygon has diagonals? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/#What_polygon_has_20_diagonals\" title=\"What polygon has 20 diagonals?\">What polygon has 20 diagonals?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span data-contrast=\"auto\">A polygon is a two-dimensional geometric shape with straight sides. The formulas associated with polygons are used to calculate various properties such as the perimeter, area, interior angles, and diagonals of the polygon. The specific formulas depend on the type of polygon, including triangles, quadrilaterals, pentagons, hexagons, and so on. These formulas provide a systematic approach to determine the measurements and characteristics of polygons, enabling us to solve problems and analyze geometric shapes effectively.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">What is Polygon? <\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">A simple closed figure formed by line segments which are in the same plane is called a <\/span><span data-contrast=\"auto\">Polygon. <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<div class=\"d-grid gap-2\"><a href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polynomial-formula\/\"> <button class=\"btn btn-primary\" style=\"width: 100%; cursor: pointer;\" type=\"button\"><strong>Also Read: Polynomial Formula<\/strong> <\/button> <\/a><\/div>\n<p><span data-contrast=\"auto\">A polygon can have any number of sides, 3, 4, 5 or 100 or even more. Based on the number <\/span><span data-contrast=\"auto\">of sides, polygons have different names.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">For example:<\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-medium wp-image-621034 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-182906-300x215.png\" alt=\"\" width=\"300\" height=\"215\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-182906-300x215.png?v=1687266121 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-182906.png?v=1687266121 460w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<h2><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<h2><b><span data-contrast=\"auto\">What are the types of polygons?<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">We know that a polygon is a simple closed figure made up of only line segments. Based on the <\/span><span data-contrast=\"auto\">number of sides or vertices in a polygon, they are known as a triangle, quadrilateral, pentagon <\/span><span data-contrast=\"auto\">and so on.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Let us look at some other types of polygons.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<div class=\"d-grid gap-2\"><a href=\"https:\/\/infinitylearn.com\/surge\/formulas\/polygon-formula\/\"> <button class=\"btn btn-primary\" style=\"width: 100%; cursor: pointer;\" type=\"button\"><strong>Also Read: Polygon Formula<\/strong> <\/button> <\/a><\/div>\n<h2><b><span data-contrast=\"auto\">What are convex and concave polygons?<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">Based on how the vertices of a polygon point, there are two types:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:240,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">(i) Convex polygon <\/span><\/b><span data-contrast=\"auto\">&#8211; It is a polygon in which any line segment joining any two <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">vertices of the polygon lies wholly in the interior of it.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-medium wp-image-621040 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-182948-300x138.png\" alt=\"\" width=\"300\" height=\"138\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-182948-300x138.png?v=1687266154 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-182948.png?v=1687266154 400w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p><b><span data-contrast=\"auto\">(ii) Concave polygon<\/span><\/b><span data-contrast=\"auto\"> &#8211; It is a polygon in which at least one of the line segment joining <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">the vertices of the polygon lies outside the polygon<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-medium wp-image-621042 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-182959-300x171.png\" alt=\"\" width=\"300\" height=\"171\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-182959-300x171.png?v=1687266164 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-182959.png?v=1687266164 421w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<div class=\"d-grid gap-2\"><a href=\"https:\/\/infinitylearn.com\/surge\/formulas\/prime-number-formula\/\"> <button class=\"btn btn-primary\" style=\"width: 100%; cursor: pointer;\" type=\"button\"><strong>Also Read: Prime Number Formula<\/strong> <\/button> <\/a><\/div>\n<h2><b><span data-contrast=\"auto\">What are Regular and Irregular polygons?<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">Based on the length of the sides, a polygon is classified as:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:240,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">(i) Regular polygon<\/span><\/b><span data-contrast=\"auto\"> &#8211; It is a polygon that has all its sides of equal length.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-621045 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-183014.png\" alt=\"\" width=\"298\" height=\"181\" \/><\/span><\/p>\n<p><b><span data-contrast=\"auto\">(ii) Irregular polygon<\/span><\/b><span data-contrast=\"auto\"> &#8211; It is a polygon that does not have all sides of equal length.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-medium wp-image-621047 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-183030-300x136.png\" alt=\"\" width=\"300\" height=\"136\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-183030-300x136.png?v=1687266188 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-183030.png?v=1687266188 394w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<div class=\"d-grid gap-2\"><a href=\"https:\/\/infinitylearn.com\/surge\/formulas\/proportion-formula\/\"> <button class=\"btn btn-primary\" style=\"width: 100%; cursor: pointer;\" type=\"button\"><strong>Also Read: Proportion Formula<\/strong> <\/button> <\/a><\/div>\n<h2><b><span data-contrast=\"auto\">Polygon Formula:<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><b><span data-contrast=\"auto\">1: Interior Angles Sum Property:<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:240,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The angle sum of a polygon for interior angles can be determined by multiplying the number of <\/span><span data-contrast=\"auto\">triangles it consists of, by 180\u00b0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The angle sum of a polygon for interior angles can be determined by multiplying the number of<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><span data-contrast=\"auto\">triangles it consists of, by 180\u00b0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-621053 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-183048.png\" alt=\"\" width=\"259\" height=\"199\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">For example, quadrilateral ABCD is made up of triangles ABC and BCD.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ul>\n<li><span data-contrast=\"auto\"> Sum of angles of triangle ABC = 180\u00b0<\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">Sum of angles of triangle BCD= 180\u00b0<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ul>\n<li><span data-contrast=\"auto\"> Therefore, sum of angles of triangle ABC + BCD = 180 + 180<\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">That is, the sum of angles of quadrilateral ABCD = 180\u00b0 x 2<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><strong>The Polygon Formulas are:<\/strong><\/p>\n<table style=\"width: 44.4115%;\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<th style=\"width: 75.2834%;\">Aspect<\/th>\n<th style=\"width: 41.2698%;\">Formula<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 75.2834%;\">Sum of Interior Angles (n-sided polygon)<\/td>\n<td style=\"width: 41.2698%;\">180\u00b0(n-2)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 75.2834%;\">Number of Diagonals (n-sided polygon)<\/td>\n<td style=\"width: 41.2698%;\">[n(n-3)]\/2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 75.2834%;\">Interior Angle Measurement (Regular n-sided)<\/td>\n<td style=\"width: 41.2698%;\">[(n-2)180\u00b0]\/n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 75.2834%;\">Exterior Angle Measurement (Regular n-sided)<\/td>\n<td style=\"width: 41.2698%;\">360\u00b0\/n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"d-grid gap-2\"><a href=\"https:\/\/infinitylearn.com\/surge\/formulas\/pyramid-formula\/\"> <button class=\"btn btn-primary\" style=\"width: 100%; cursor: pointer;\" type=\"button\"><strong>Also Read: Pyramid Formula<\/strong> <\/button> <\/a><\/div>\n<h2><b><span data-contrast=\"auto\">um of angles of a pentagon<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">A pentagon can be divided into 3 triangles. Hence, the sum of its angles = 180\u00b0 x 3<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-621056 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-183111.png\" alt=\"\" width=\"276\" height=\"169\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Let us look at the relationship between the number of sides of a polygon and its angle sum.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-medium wp-image-621060 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-183122-300x195.png\" alt=\"\" width=\"300\" height=\"195\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-183122-300x195.png?v=1687266253 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-183122.png?v=1687266253 487w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">This can be generalized as:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The sum of angles of a polygon having \u2018n\u2019 sides is given by (n &#8211; 2) x 180\u00b0.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">2: Number of diagonals of a polygon:<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Diagonals of a polygon are line segments connecting non-adjacent vertices. The number of diagonals in a polygon can be found using the formula n(n-3)\/2, where n is the number of sides. For instance, a hexagon has six sides, so the number of diagonals is (6(6-3))\/2 = 9.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Solved Examples on Polygon Formula:<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><b><span data-contrast=\"auto\">Example 1: <\/span><\/b><span data-contrast=\"auto\">Determine the sum of interior angles and the number of diagonals in an octagon.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Sum of interior angles = (n &#8211; 2) \u00d7 180 degrees = (8 &#8211; 2) \u00d7 180 = 1080 degrees<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Number of diagonals = n \u00d7 (n &#8211; 3) \/ 2 = 8 \u00d7 (8 &#8211; 3) \/ 2 = 20 diagonals<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">Example 2: <\/span><\/b><span data-contrast=\"auto\">Calculate the area of an irregular triangle with a base length of 12 cm and a height of 8 cm.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Area of a triangle = (1\/2) \u00d7 base \u00d7 height = (1\/2) \u00d7 12 \u00d7 8 = 48 cm\u00b2<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">Example 3: <\/span><\/b><span data-contrast=\"auto\">Find the perimeter of a quadrilateral with side lengths 5 cm, 6 cm, 7 cm, and 8 cm.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Perimeter of a quadrilateral = sum of all side lengths = 5 + 6 + 7 + 8 = 26 cm<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">Example 4:<\/span><\/b><span data-contrast=\"auto\"> Determine the number of diagonals in a decagon.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Number of diagonals = n \u00d7 (n &#8211; 3) \/ 2 = 10 \u00d7 (10 &#8211; 3) \/ 2 = 35 diagonals<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Frequently Asked Questions on Polygon Formula:<\/span><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">1: What is sum of all angles of polygon?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: The sum of all angles in a polygon is given by the formula (n-2) \u00d7 180 degrees, where n represents the number of sides or vertices of the polygon.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">2: What is the formula for finding the diagonals of a polygon?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: The formula for finding the number of diagonals in a polygon is given by the expression n \u00d7 (n-3) \/ 2, where n represents the number of sides or vertices of the polygon. It calculates the number of line segments that can be drawn connecting any two non-adjacent vertices of the polygon.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">3: What is the formula of area of polygon?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: The formula for calculating the area of a polygon depends on the type of polygon. For regular polygons, the formula is (1\/2) \u00d7 apothem \u00d7 perimeter, where the apothem is the distance from the center of the polygon to any side, and the perimeter is the sum of all the side lengths. For irregular polygons, the area can be determined by dividing the polygon into smaller, regular shapes and summing their individual areas.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">4: Which polygon has 20 diagonals?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: A polygon with 20 diagonals is an octagon. An octagon has eight sides and using the formula for calculating the number of diagonals in a polygon, which is n \u00d7 (n-3) \/ 2, we can substitute the value of n as 8. Thus, the octagon has 8 \u00d7 (8-3) \/ 2 = 20 diagonals.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">5: What is the formula for the length of diagonal?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: The formula for calculating the length of a diagonal in a polygon depends on the specific polygon and the information given. However, if the polygon is regular and you know the side length, you can use trigonometric functions to calculate the length of a diagonal.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">6: What polygon has 7 diagonals?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: A polygon with 7 diagonals is a pentagon (a polygon with five sides). By using the formula for calculating the number of diagonals in a polygon, which is n \u00d7 (n-3) \/ 2, we can substitute the value of n as 5. Therefore, a pentagon has 5 \u00d7 (5-3) \/ 2 = 7 diagonals.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">7: What is the difference between regular and irregular polygons?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: Regular polygons have equal side lengths and angles, while irregular polygons have varying side lengths and\/or angles. Regular polygons exhibit symmetry and have a uniform shape, whereas irregular polygons lack symmetry and do not have a consistent shape.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">8: What is the difference between concave and convex polygons?<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: Concave polygons have at least one interior angle greater than 180 degrees, with &#8220;caved-in&#8221; or &#8220;hollow&#8221; portions. Convex polygons have all interior angles less than 180 degrees, with no &#8220;caved-in&#8221; portions and outward-pointing vertices. Concave polygons exhibit inward curvature, while convex polygons exhibit outward curvature.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Polygon_Formula_FAQs\"><\/span>Polygon Formula FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_do_you_find_the_sides_of_a_polygon\"><\/span>How do you find the sides of a polygon?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tTo find the sides of a polygon, count the number of line segments that form its shape. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_do_you_solve_a_polygon_formula\"><\/span>How do you solve a polygon formula?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tYou solve a polygon formula by using the specific mathematical rule or equation that corresponds to the shape's characteristics.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_polygon_in_math_7\"><\/span>What is polygon in math 7? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIn math, a polygon with 7 sides is called a heptagon.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_formula_for_the_area_of_a_polygon_with_n_sides\"><\/span>What is the formula for the area of a polygon with n sides?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe formula for finding the area of a polygon with n sides varies based on the shape's type and dimensions.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_area_of_a_polygon_with_5_sides\"><\/span>What is the area of a polygon with 5 sides? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe area of a 5-sided polygon depends on its shape and dimensions; a specific formula is needed. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_formula_for_regular_polygon\"><\/span>What is the formula for regular polygon?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA regular polygon is one with equal sides and angles, making it easier to calculate its properties.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Which_polygon_has_diagonals\"><\/span>Which polygon has diagonals? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tMany polygons have diagonals, but squares, rectangles, and triangles are common examples. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_polygon_has_20_diagonals\"><\/span>What polygon has 20 diagonals?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA polygon with 20 diagonals is typically a dodecagon (12 sides) or a polygon with a large number of sides to have that many diagonals.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How do you find the sides of a polygon?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"To find the sides of a polygon, count the number of line segments that form its shape.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How do you solve a polygon formula?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"You solve a polygon formula by using the specific mathematical rule or equation that corresponds to the shape's characteristics.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is polygon in math 7? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"In math, a polygon with 7 sides is called a heptagon.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the formula for the area of a polygon with n sides?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The formula for finding the area of a polygon with n sides varies based on the shape's type and dimensions.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the area of a polygon with 5 sides? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The area of a 5-sided polygon depends on its shape and dimensions; a specific formula is needed.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the formula for regular polygon?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A regular polygon is one with equal sides and angles, making it easier to calculate its properties.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Which polygon has diagonals? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Many polygons have diagonals, but squares, rectangles, and triangles are common examples.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What polygon has 20 diagonals?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A polygon with 20 diagonals is typically a dodecagon (12 sides) or a polygon with a large number of sides to have that many diagonals.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>A polygon is a two-dimensional geometric shape with straight sides. The formulas associated with polygons are used to calculate various [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Polygon Formula\u00a0","_yoast_wpseo_title":"What is polygon formula - Examples, Formulas,","_yoast_wpseo_metadesc":"Learn the polygon definition here. Also, get the various types of a polygon, its properties, formulas with a solved example.","custom_permalink":"formulas\/polygon-formula\/"},"categories":[8438,8536],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is polygon formula - Examples, Formulas,<\/title>\n<meta name=\"description\" content=\"Learn the polygon definition here. 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