{"id":1538,"date":"2022-04-20T08:34:06","date_gmt":"2022-04-20T08:34:06","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1538"},"modified":"2023-05-26T09:56:09","modified_gmt":"2023-05-26T09:56:09","slug":"diagonal-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/diagonal","title":{"rendered":"Diagonal &#8211; Definition with Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-4d4f929d-0091-48a1-b18b-a10bdd41f791\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/diagonal#0-diagonals-in-geometry>Diagonals in Geometry<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/diagonal#2-diagonals-of-polygon>Diagonals of Polygon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/diagonal#3-diagonals-of-solid-shapes>Diagonals of Solid Shapes<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/diagonal#5-solved-examples-on-diagonals>Solved Examples on Diagonals<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/diagonal#6-practice-problems-on-diagonals>Practice Problems on Diagonals<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/diagonal#7-frequently-asked-questions-on-diagonals>Frequently Asked Questions on Diagonals<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-diagonals-in-geometry\">Diagonals in Geometry<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polygon\">polygon<\/a> is defined as a flat or plane, two-dimensional <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/closed-shape\">closed shape<\/a> bounded with straight sides. A diagonal is a line segment connecting the opposite vertices (or corners) of a polygon. In other words, a diagonal is a line segment connecting two non-adjacent vertices of a polygon. It joins the vertices of a polygon, excluding the edges of the figure. The following shapes have a diagonal drawn on them:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-1.png\" alt=\"Diagonals in Geometry\" class=\"wp-image-5669\" width=\"620\" height=\"314\" title=\"Diagonals in Geometry\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-1-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-history-of-the-diagonal\">History of the Diagonal<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The word diagonal comes from the ancient Greek word <em>diagonios<\/em>, which means &#8220;from angle to angle.&#8221; Both Euclid and Strabo used it to describe a line that connects two vertices of a cuboid or a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/rhombus\" target=\"_blank\" rel=\"noopener\" title=\"\">rhombus<\/a>; later, it became known in Latin as <em>diagonus<\/em> (slanting line).<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-diagonals-of-polygon\">Diagonals of Polygon<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Diagonal Formula<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Diagonals for polygons of all <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/shape\" target=\"_blank\" rel=\"noopener\" title=\"\">shapes<\/a> and sizes can be made and for every shape; there is a formula to determine the number of diagonals.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The number of diagonals in a polygon with n vertices = $\\frac{n(n-3)}{2}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-2.png\" alt=\"Number of diagonals in a polygon with n vertices\" class=\"wp-image-5670\" title=\"Number of diagonals in a polygon with n vertices\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-2-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">So, from this formula, we can easily calculate the number of diagonals in a polygon.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The given table shows the number of diagonals in different polygons:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"307\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-3.png\" alt=\"Number of diagonals in different polygons\" class=\"wp-image-5671\" title=\"Number of diagonals in different polygons\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-3-300x149.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-diagonals-of-solid-shapes\">Diagonals of Solid Shapes<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Just like polygons, solid or <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/3-dimensional\" target=\"_blank\" rel=\"noopener\" title=\"\">3D shapes<\/a> also have diagonals. Based on the number of edges, the number and properties of diagonals vary for different solids. The following solids have some diagonals drawn on them:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"314\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-5.png\" alt=\"Diagonals of Solid Shapes\" class=\"wp-image-5672\" title=\"Diagonals of Solid Shapes\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-5-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-length-of-a-diagonal\">Length of a Diagonal<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The length of diagonals of any shape depends on the dimensions of its sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Length of Diagonal of Square<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The length of the diagonal of a square can be derived using the Pythagoras theorem. A diagonal of a square divides it into two right-angled triangles. Applying the Pythagoras theorem, we can find the length of the diagonal (d) of a square with side (a) as a$\\sqrt{2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Diagonal length of a square with each side a units&nbsp; =  a$\\sqrt{2}$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Length of Diagonal of Rectangle<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"312\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-6-1.png\" alt=\"Length of Diagonal of Rectangle\" class=\"wp-image-5674\" title=\"Length of Diagonal of Rectangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-6-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Diagonal-6-1-300x151.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">A diagonal of a rectangle divides it into two <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-triangle\" target=\"_blank\" rel=\"noopener\" title=\"\">right-angled triangles<\/a>. Applying the Pythagoras theorem, we can find the length of diagonal of a rectangle with <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/length\" target=\"_blank\" rel=\"noopener\" title=\"\">length<\/a> (l) and breadth (b) as<\/p>\n\n\n\n<p class=\"eplus-wrapper\">d$^{2}$ = l$^{2}$ + b$^{2}$&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, d = $\\sqrt{l^{2} + b^{2}}$, where d is diagonal, l is length, and b is the breadth of the rectangle.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-solved-examples-on-diagonals\">Solved Examples on Diagonals<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>What is the total number of diagonals in a polygon of 12 sides?<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The number of diagonals in a polygon with n vertices = $\\frac{n(n-3)}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the number of diagonals in a polygon with 12 sides&nbsp; = $\\frac{12(12-3)}{2}$ = 54<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>What is the length of the diagonal of a square with each side 6 cm long?<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Side, a = 6 cm<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Length of the diagonal = a $\\times \\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 6 $\\times \\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =&nbsp; 6$\\sqrt{2}$ cm<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Rahul is strolling across a rectangular park that is 20 meters long and 15 meters wide. Determine the diagonal of the rectangular park.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Length of the rectangular park = 20 m, Breadth of the rectangular park = 15 m<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Length of the diagonal = $\\sqrt{l^{2} + b^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = $\\sqrt{20^{2} + 15^{2}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= $\\sqrt{400 + 225}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;        = $\\sqrt{625}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 25 m<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-practice-problems-on-diagonals\">Practice Problems on Diagonals<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Diagonal<\/h2><p style=\"display:none;\">Attend this Quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the total number of diagonals in a hexagon?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5<\/div><div class=\"spq_answer_block\" data-value=\"1\">6<\/div><div class=\"spq_answer_block\" data-value=\"2\">8<\/div><div class=\"spq_answer_block\" data-value=\"3\">9<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 9<br\/>Number of diagonals in hexagon (6 vertices) = $\\frac{6(6-3)}{2}$ = 9<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The length of the rectangle is thrice its breadth. Which of the following is the diagonal length if the rectangle's breadth is 2 cm?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\sqrt{10}$ cm<\/div><div class=\"spq_answer_block\" data-value=\"1\">2$\\sqrt{10}$ cm<\/div><div class=\"spq_answer_block\" data-value=\"2\">10 cm<\/div><div class=\"spq_answer_block\" data-value=\"3\">20 cm<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 2$\\sqrt{10}$ cm<br\/>Breadth and Length of the rectangle is 2 cm and 6 cm respectively.<br>\r\nLength of the Diagonal = $\\sqrt{2^{2} + 6^{2}}$ = $\\sqrt{4+36}$ = $\\sqrt{40}$ = $2\\sqrt{10}$ cm<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following is the perimeter of the square whose diagonal is 6$\\sqrt{2}$ cm long?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">6 cm<\/div><div class=\"spq_answer_block\" data-value=\"1\">24 cm<\/div><div class=\"spq_answer_block\" data-value=\"2\">3$\\sqrt{2}$ cm<\/div><div class=\"spq_answer_block\" data-value=\"3\">24$\\sqrt{2}$ cm<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 24 cm<br\/>Diagonal of a square with side length a is a$\\sqrt{2}$ . Since a$\\sqrt{2}$ = 6$\\sqrt{2}$, a must be 6 cm. <br> \r\nTherefore, the perimeter of the square must be 4 \u00d7 6 cm or 24 cm.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this Quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Diagonal\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Diagonal\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the total number of diagonals in a hexagon?\",\n                    \"text\": \"What is the total number of diagonals in a hexagon?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Number of diagonals in hexagon (6 vertices) = $$\\\\frac{6(6-3)}{2}$$ = 9\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Number of diagonals in hexagon (6 vertices) = $$\\\\frac{6(6-3)}{2}$$ = 9\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Number of diagonals in hexagon (6 vertices) = $$\\\\frac{6(6-3)}{2}$$ = 9\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Number of diagonals in hexagon (6 vertices) = $$\\\\frac{6(6-3)}{2}$$ = 9\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"9\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Number of diagonals in hexagon (6 vertices) = $$\\\\frac{6(6-3)}{2}$$ = 9\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Number of diagonals in hexagon (6 vertices) = $$\\\\frac{6(6-3)}{2}$$ = 9\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The length of the rectangle is thrice its breadth. Which of the following is the diagonal length if the rectangle's breadth is 2 cm?\",\n                    \"text\": \"The length of the rectangle is thrice its breadth. Which of the following is the diagonal length if the rectangle's breadth is 2 cm?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Breadth and Length of the rectangle is 2 cm and 6 cm respectively.<br>\r\nLength of the Diagonal = $$\\\\sqrt{2^{2} + 6^{2}}$$ = $$\\\\sqrt{4+36}$$ = $$\\\\sqrt{40}$$ = $$2\\\\sqrt{10}$$ cm\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\sqrt{10}$$ cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Breadth and Length of the rectangle is 2 cm and 6 cm respectively.<br>\r\nLength of the Diagonal = $$\\\\sqrt{2^{2} + 6^{2}}$$ = $$\\\\sqrt{4+36}$$ = $$\\\\sqrt{40}$$ = $$2\\\\sqrt{10}$$ cm\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10 cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Breadth and Length of the rectangle is 2 cm and 6 cm respectively.<br>\r\nLength of the Diagonal = $$\\\\sqrt{2^{2} + 6^{2}}$$ = $$\\\\sqrt{4+36}$$ = $$\\\\sqrt{40}$$ = $$2\\\\sqrt{10}$$ cm\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"20 cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Breadth and Length of the rectangle is 2 cm and 6 cm respectively.<br>\r\nLength of the Diagonal = $$\\\\sqrt{2^{2} + 6^{2}}$$ = $$\\\\sqrt{4+36}$$ = $$\\\\sqrt{40}$$ = $$2\\\\sqrt{10}$$ cm\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"2$$\\\\sqrt{10}$$ cm\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Breadth and Length of the rectangle is 2 cm and 6 cm respectively.<br>\r\nLength of the Diagonal = $$\\\\sqrt{2^{2} + 6^{2}}$$ = $$\\\\sqrt{4+36}$$ = $$\\\\sqrt{40}$$ = $$2\\\\sqrt{10}$$ cm\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Breadth and Length of the rectangle is 2 cm and 6 cm respectively.<br>\r\nLength of the Diagonal = $$\\\\sqrt{2^{2} + 6^{2}}$$ = $$\\\\sqrt{4+36}$$ = $$\\\\sqrt{40}$$ = $$2\\\\sqrt{10}$$ cm\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is the perimeter of the square whose diagonal is 6$$\\\\sqrt{2}$$ cm long?\",\n                    \"text\": \"Which of the following is the perimeter of the square whose diagonal is 6$$\\\\sqrt{2}$$ cm long?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Diagonal of a square with side length a is a$$\\\\sqrt{2}$$ . Since a$$\\\\sqrt{2}$$ = 6$$\\\\sqrt{2}$$, a must be 6 cm. <br> \r\nTherefore, the perimeter of the square must be 4 \u00d7 6 cm or 24 cm.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6 cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Diagonal of a square with side length a is a$$\\\\sqrt{2}$$ . Since a$$\\\\sqrt{2}$$ = 6$$\\\\sqrt{2}$$, a must be 6 cm. <br> \r\nTherefore, the perimeter of the square must be 4 \u00d7 6 cm or 24 cm.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3$$\\\\sqrt{2}$$ cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Diagonal of a square with side length a is a$$\\\\sqrt{2}$$ . Since a$$\\\\sqrt{2}$$ = 6$$\\\\sqrt{2}$$, a must be 6 cm. <br> \r\nTherefore, the perimeter of the square must be 4 \u00d7 6 cm or 24 cm.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"24$$\\\\sqrt{2}$$ cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Diagonal of a square with side length a is a$$\\\\sqrt{2}$$ . Since a$$\\\\sqrt{2}$$ = 6$$\\\\sqrt{2}$$, a must be 6 cm. <br> \r\nTherefore, the perimeter of the square must be 4 \u00d7 6 cm or 24 cm.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"24 cm\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Diagonal of a square with side length a is a$$\\\\sqrt{2}$$ . Since a$$\\\\sqrt{2}$$ = 6$$\\\\sqrt{2}$$, a must be 6 cm. <br> \r\nTherefore, the perimeter of the square must be 4 \u00d7 6 cm or 24 cm.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Diagonal of a square with side length a is a$$\\\\sqrt{2}$$ . Since a$$\\\\sqrt{2}$$ = 6$$\\\\sqrt{2}$$, a must be 6 cm. <br> \r\nTherefore, the perimeter of the square must be 4 \u00d7 6 cm or 24 cm.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-frequently-asked-questions-on-diagonals\">Frequently Asked Questions on Diagonals<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-4795b5da-8eb1-4bb4-b8b3-bf07b5ac78ef\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-4795b5da-8eb1-4bb4-b8b3-bf07b5ac78ef\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4795b5da-8eb1-4bb4-b8b3-bf07b5ac78ef\"><strong>Which polygon has an equal number of sides and diagonals?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-4795b5da-8eb1-4bb4-b8b3-bf07b5ac78ef\">\n\n<p>A pentagon has five sides and five diagonals. &lt;br&gt;<\/p>\n\n\n\n<p>Number of diagonals in a polygon with n vertices = $\\frac{n(n-3)}{2}$ &lt;br&gt;<br>Number of diagonals in a pentagon = $\\frac{5(5-3)}{2}$ = 5<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-4795b5da-8eb1-4bb4-b8b3-bf07b5ac78ef\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4795b5da-8eb1-4bb4-b8b3-bf07b5ac78ef\"><strong>Why does the triangle not have any diagonal?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-4795b5da-8eb1-4bb4-b8b3-bf07b5ac78ef\">\n\n<p>A polygon&#8217;s diagonal is a line connecting a vertex to a non-adjacent vertex. As a result, the simplest polygon, a triangle, seems to have no diagonals. We can&#8217;t connect a line from one internal angle to another that isn&#8217;t also a side of the triangle.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-4795b5da-8eb1-4bb4-b8b3-bf07b5ac78ef\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4795b5da-8eb1-4bb4-b8b3-bf07b5ac78ef\"><strong>Which quadrilaterals have diagonals that bisect each other?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-4795b5da-8eb1-4bb4-b8b3-bf07b5ac78ef\">\n\n<p>When each diagonal of a polygon cuts the other diagonal into two equal parts, they are said to bisect each other. The <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/quadrilateral\" target=\"_blank\" rel=\"noopener\" title=\"\">quadrilaterals<\/a> with bisecting diagonals are <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/rectangle\" target=\"_blank\" rel=\"noopener\" title=\"\">rectangle<\/a>, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/square\" target=\"_blank\" rel=\"noopener\" title=\"\">square<\/a>, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallelogram\" target=\"_blank\" rel=\"noopener\" title=\"\">parallelogram<\/a>, and rhombus.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Diagonals in Geometry A polygon is defined as a flat or plane, two-dimensional closed shape bounded with straight sides. A diagonal is a line segment connecting the opposite vertices (or corners) of a polygon. In other words, a diagonal is a line segment connecting two non-adjacent vertices of a polygon. It joins the vertices of &#8230; <a title=\"Diagonal &#8211; Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/diagonal\" aria-label=\"More on Diagonal &#8211; Definition with Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1538","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1538","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=1538"}],"version-history":[{"count":14,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1538\/revisions"}],"predecessor-version":[{"id":29502,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1538\/revisions\/29502"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1538"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1538"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1538"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}