{"id":620849,"date":"2023-06-20T18:13:11","date_gmt":"2023-06-20T12:43:11","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=620849"},"modified":"2025-02-28T17:13:50","modified_gmt":"2025-02-28T11:43:50","slug":"620849-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/formulas\/diagonal-formula\/","title":{"rendered":"Diagonal 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\/diagonal-formula\/#Diagonal_Formulas\" title=\"Diagonal Formulas: \">Diagonal Formulas: <\/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\/diagonal-formula\/#Solved_Examples_on_Diagonal_Formula\" title=\"Solved Examples on Diagonal Formula: \">Solved Examples on Diagonal Formula: <\/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\/diagonal-formula\/#Frequently_Asked_Questions_on_Diagonal_Formula\" title=\"Frequently Asked Questions on Diagonal Formula: \">Frequently Asked Questions on Diagonal Formula: <\/a><\/li><\/ul><\/nav><\/div>\n<p><span data-contrast=\"auto\">A diagonal is a line segment that connects two non-adjacent vertices of a polygon. It traverses the interior of the polygon, creating additional line segments within it. Diagonals play a significant role in geometry, aiding in the measurement of distances, determining angles, and dividing shapes into smaller parts. Formulas for diagonal lengths vary depending on the polygon&#8217;s type and properties.<\/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><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\">Diagonal Formulas:<\/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\">The formula for calculating the length of the diagonal of a quadrilateral depends on the type of quadrilateral. Here are the diagonal formulas for some common quadrilaterals:<\/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<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,0],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><b><span data-contrast=\"auto\">Rectangle:<\/span><\/b><span data-contrast=\"auto\"> In a rectangle, the diagonals are equal in length. For a rectangle with length (l) and width (w), the length of the diagonal (d) can be calculated using the formula: <\/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><\/li>\n<\/ol>\n<p><span data-contrast=\"auto\">d = \u221a(l<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> + w<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,0],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><b><span data-contrast=\"auto\">Square:<\/span><\/b><span data-contrast=\"auto\"> In a square, all sides are equal, and the diagonals are equal as well. For a square with side length (s), the length of the diagonal (d) can be calculated using the formula: <\/span><br \/>\n<span data-contrast=\"auto\">d = s\u221a2<\/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><\/li>\n<\/ol>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,0],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"3\" data-aria-level=\"1\"><b><span data-contrast=\"auto\">Parallelogram<\/span><\/b><span data-contrast=\"auto\">: In a parallelogram, the diagonals bisect each other, dividing the parallelogram into four congruent triangles. The length of the diagonal (d1 or d2) can be calculated using the formula: <\/span><br \/>\n<span data-contrast=\"auto\">d1 = \u221a(a<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> + b<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> &#8211; 2abcos\u03b8) <\/span><br \/>\n<span data-contrast=\"auto\">d2 = \u221a(c<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> + d<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> &#8211; 2cdcos\u03b8)<\/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><\/li>\n<\/ol>\n<p><span data-contrast=\"auto\">where a and b are the lengths of the adjacent sides, c and d are the lengths of the other adjacent sides, and \u03b8 is the angle between those adjacent sides.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,0],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"4\" data-aria-level=\"1\"><span data-contrast=\"auto\">T<\/span><b><span data-contrast=\"auto\">rapezoid:<\/span><\/b><span data-contrast=\"auto\"> In a trapezoid, the diagonals do not have a simple formula. The lengths of the diagonals depend on the lengths of the bases and the height of the trapezoid.<\/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><\/li>\n<\/ol>\n<p><span data-contrast=\"auto\">These diagonal formulas provide a way to calculate the length of the diagonals for specific quadrilaterals. Understanding these formulas allows for the determination of diagonal lengths, which can be useful in various geometric calculations and constructions.<\/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><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Solved Examples on Diagonal Formula:<\/span><\/b><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&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\">Given a rectangle with a length of 6 units and a width of 4 units, calculate the length of the diagonal.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&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;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Using the diagonal formula for a rectangle:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = \u221a(l<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> + w<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">)<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = \u221a(6<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> + 4<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">)<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = \u221a(36 + 16)<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = \u221a52<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d \u2248 7.211<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Therefore, the length of the diagonal in this rectangle is approximately 7.211 units.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&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\"> If a square has a side length of 10 units, determine the length of the diagonal.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&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;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Using the diagonal formula for a square:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = s\u221a2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = 10\u221a2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d \u2248 14.142<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Hence, the length of the diagonal in this square is approximately 14.142 units.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&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\">Consider a parallelogram with adjacent sides measuring 8 units and 5 units, and an angle of 60 degrees between them. Calculate the length of one of its diagonals.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&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;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Using the diagonal formula for a parallelogram:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = \u221a(a<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> + b<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> &#8211; 2abcos\u03b8)<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = \u221a(8<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> + 5<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> &#8211; 2 x 8 x 5 x cos 60\u00b0)<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = \u221a(64 + 25 &#8211; 80 x 0.5)<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = \u221a(64 + 25 &#8211; 40)<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = \u221a49<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">d = 7<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Therefore, the length of one of the diagonals in this parallelogram is 7 units.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Frequently Asked Questions on Diagonal Formula:<\/span><\/b><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">1: What is diagonal in polygon?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: In a polygon, a diagonal is a line segment that connects two non-adjacent vertices. It is a line that lies completely inside the polygon, crossing through its interior. Diagonals divide the polygon into smaller triangles or quadrilaterals, and they can provide information about the shape&#8217;s internal structure and properties. Diagonals are particularly relevant in polygons with four or more sides, such as quadrilaterals, pentagons, and hexagons.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">2: What is diagonal in square?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: In a square, a diagonal is a line segment that connects two opposite vertices. It is a line that passes through the interior of the square, dividing it into two congruent right triangles. The length of the diagonal in a square can be calculated using the Pythagorean theorem. If the side length of the square is &#8220;s,&#8221; then the length of the diagonal (d) can be found as d = s\u221a2.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">3: Are diagonals of a square equal?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: Yes, the diagonals of a square are equal in length. In a square, there are two diagonals that connect opposite vertices. These diagonals bisect each other at a right angle, dividing the square into four congruent right triangles. Since a square has all sides equal in length and all angles equal to 90 degrees, the diagonals are also of equal length. Therefore, in a square, both diagonals have the same length.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">4: What is the number of diagonals in 7-sided polygon?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: The number of diagonals in a polygon can be calculated using the formula:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Number of diagonals = (n x (n &#8211; 3)) \/ 2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Where &#8220;n&#8221; represents the number of sides of the polygon.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">For a 7-sided polygon, applying the formula:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Number of diagonals = (7 x (7 &#8211; 3)) \/ 2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">= (7 x 4) \/ 2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">= 28 \/ 2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">= 14<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Therefore, a 7-sided polygon has 14 diagonals.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">5: Which polygon has 20 diagonals?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: To determine which polygon has 20 diagonals, we can rearrange the formula for the number of diagonals in a polygon:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">(n x (n &#8211; 3)) \/ 2 = 20<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Multiplying both sides by 2 gives: <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">n x (n &#8211; 3) = 40 <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Expanding the equation:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">n<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> &#8211; 3n = 40<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Rearranging the equation to the quadratic form:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">n<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> &#8211; 3n &#8211; 40 = 0<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Now we need to find the values of &#8220;n&#8221; that satisfy this equation. By factoring or using the quadratic formula, we find that &#8220;n&#8221; can be either -5 or 8. However, since we&#8217;re considering the number of sides of a polygon, &#8220;n&#8221; must be a positive integer. Therefore, the polygon that has 20 diagonals is an 8-sided polygon, also known as an octagon.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">6: Which polygon has no diagonals?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: A polygon with only three sides, known as a triangle, has no diagonals. In a triangle, all three sides are already connected, so there are no additional line segments that can be drawn within the polygon without overlapping with the sides.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">7: How many diagonals can a polygon have?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: A polygon with &#8220;n&#8221; sides can have a maximum of (n x (n-3))\/2 diagonals. This formula counts all the possible line segments that can be drawn between non-adjacent vertices within the polygon. Note that this count includes the sides of the polygon as well.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">8: Does regular polygon have equal diagonals?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: Yes, in a regular polygon, all diagonals are of equal length. A regular polygon is a polygon in which all sides and angles are equal. Since the sides of a regular polygon are equal, the diagonals that connect non-adjacent vertices will also be equal in length. This symmetry is a defining characteristic of regular polygons.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A diagonal is a line segment that connects two non-adjacent vertices of a polygon. It traverses the interior of the [&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":"Diagonal Formula","_yoast_wpseo_title":"Diagonal Formula - Definition, Derivation, and Examples","_yoast_wpseo_metadesc":"Understand the diagonal formula for geometric shapes. 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