{"id":27377,"date":"2023-04-12T02:37:59","date_gmt":"2023-04-12T02:37:59","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=27377"},"modified":"2024-02-05T16:11:30","modified_gmt":"2024-02-05T16:11:30","slug":"diagonal-of-a-square-definition-formula-properties-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-a-square","title":{"rendered":"Diagonal of a Square &#8211; Definition, Formula, Properties, Examples"},"content":{"rendered":"<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-8cc93e8d-d5bc-4fe2-b3e9-8ab7eea26321\" 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\/diagonal-of-a-square#0-what-is-the-diagonal-of-a-square>What Is the Diagonal of a Square?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-a-square#2-properties-of-the-diagonal-of-a-square>Properties of the Diagonal of a Square<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-a-square#6-methods-to-calculate-diagonal-of-square>Methods to Calculate Diagonal of Square<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-a-square#12-solved-examples-on-diagonals-of-a-square>Solved Examples on Diagonals of a Square<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-a-square#13-practice-problems-on-diagonals-of-a-square>Practice Problems on Diagonals of a Square<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-a-square#14-frequently-asked-questions-on-diagonals-of-a-square>Frequently Asked Questions on Diagonals of a Square<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-diagonal-of-a-square\">What Is the Diagonal of a Square?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Diagonals of a square are the line segments joining opposite vertices.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">A flat, closed shape with four equal sides, four vertices (like craft paper, a photo frame), and four right angles is known as a square. Take a look at the square craft paper shown below. Let\u2019s connect two opposite corners. The two lines are called diagonals of a square.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"335\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/diagonals-of-a-square-example-with-craft-paper.png\" alt=\"Diagonals of a square: example with craft paper\" class=\"wp-image-37531\" title=\"Diagonals of a square: example with craft paper\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/diagonals-of-a-square-example-with-craft-paper.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/diagonals-of-a-square-example-with-craft-paper-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-diagonal-of-a-square-definition\">Diagonal of a Square Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper\"><strong>The diagonal of a square is a line that connects one corner to the opposite corner through the center.<\/strong> In other words, we can say that the diagonal is the slant line that connects the square&#8217;s opposite corners.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">A square has two diagonals that are equal in length. They bisect each other at right angles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"374\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/two-diagonals-of-a-square.png\" alt=\"Two diagonals of a square\" class=\"wp-image-37535\" title=\"Two diagonals of a square\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/two-diagonals-of-a-square.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/two-diagonals-of-a-square-300x181.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-with-unit-squares-and-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_unit_sq_side_length_pt.png\" alt=\"Area with Unit Squares and Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area with Unit Squares and Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-squares-and-trapezoids-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_square_trapezoid_2_pt.png\" alt=\"Classify Squares and Trapezoids as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Squares and Trapezoids as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-area-in-square-units\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_grannys_rescue_1_2_gm.png\" alt=\"Find Area in Square Units Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Area in Square Units Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-area-with-unit-squares\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_unit_square_2_pt.png\" alt=\"Find the Area with Unit Squares Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Area with Unit Squares Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-perimeter-of-the-squared-and-the-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_peri_rectangle_2_pt.png\" alt=\"Find the Perimeter of the Squared and the Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Perimeter of the Squared and the Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-kite-squares-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_square_rectangle_pt.png\" alt=\"Identify Kite, Squares and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Kite, Squares and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-squares-and-trapezoids\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_19_21_gm.png\" alt=\"Identify Squares and Trapezoids Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Squares and Trapezoids Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-the-area-with-unit-squares\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_unit_square_1_pt.png\" alt=\"Identify the Area with Unit Squares Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify the Area with Unit Squares Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-the-perimeter-with-unit-squares\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_peri_unit_square_2_pt.png\" alt=\"Identify the Perimeter with Unit Squares Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify the Perimeter with Unit Squares Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-triangles-and-squares\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangles_squares_pt.png\" alt=\"Identify Triangles and Squares Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Triangles and Squares Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-properties-of-the-diagonal-of-a-square\">Properties of the Diagonal of a Square<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"297\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/properties-of-the-diagonals-of-a-square.png\" alt=\"Properties of the diagonals of a square\" class=\"wp-image-37533\" title=\"Properties of the diagonals of a square\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/properties-of-the-diagonals-of-a-square.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/properties-of-the-diagonals-of-a-square-300x144.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The diagonal of a square is a line segment that connects any two non-adjacent vertices (corners).<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Here, AC and BD are diagonals.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The diagonals of a square are equal in length.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$AC = BD$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The square is divided into two congruent right-angle isosceles triangles by its diagonal.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Two diagonals of a square bisect each other at right angles.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When the diagonals meet the vertices of a square, they form a 45-degree angle. In other words, they bisect each pair of opposite angles.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Pythagoras\u2019 theorem can also be used to determine the length of the diagonals of a square.<\/li>\n<\/ul>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/squares-and-circles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/squares-and-circles.jpeg\" alt=\"Squares and Circles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-diagonal-of-a-square-formula\">Diagonal of a Square Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The formula for the diagonal of a square is given by the product of side length and the square root of 2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Mathematically, the diagonal of a square formula is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d = a\\times\\sqrt{2} = \\sqrt{2} a$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">where,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d =$ length of diagonal of a square&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a =$ side length of the square.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-derivation-of-diagonal-of-square-formula\">Derivation of Diagonal of Square Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s derive the diagonal of a square formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us assume that the side length of a square is \u201ca\u201d and the length of the diagonal is \u201cd.\u201d<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"476\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-diagonal-of-a-square-divides-it-into-two-right-angles.png\" alt=\"A diagonal of a square divides it into two right angles\" class=\"wp-image-37534\" title=\"A diagonal of a square divides it into two right angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-diagonal-of-a-square-divides-it-into-two-right-angles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-diagonal-of-a-square-divides-it-into-two-right-angles-300x230.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In the above figure, a square is divided into two right-angle triangles. Let\u2019s consider triangle ABC.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In $\\Delta ABC,\\; \\angleB = 90^\\circ$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Note that the diagonal AC acts as a hypotenuse of the right triangle ABC.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, now in $\\Delta ABC$ apply Pythagoras\u2019 theorem,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$AC^2 = AB^2 + BC^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d^2 = a^2 + a^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d^2 = 2a^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d = \\sqrt{2a^2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$d = a\\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, diagonal \u201cd\u201d of square is given by $d = a\\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">where \u201cd\u201d is the diagonal length and \u201ca\u201d is the side-length of the square.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-how-to-find-the-diagonal-of-a-square\">How to Find the Diagonal of a Square<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">How to calculate the length of diagonal of a square? What is the diagonal measurement of a square? Finding the diagonal of a square is simple once you know the formula! Use the diagonal of a square formula. Multiply the length of the side by $\\sqrt{2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Length of the diagonal of a square <\/strong>$=$<strong> Length of the side of the square <\/strong>$\\times\\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To get an estimate, we can use $\\sqrt{2}\\simeq 1.41$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-methods-to-calculate-diagonal-of-square\">Methods to Calculate Diagonal of Square<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The diagonal of a square can be calculated in three different ways.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"7-method-1-when-the-side-length-of-square-is-given\"><strong>Method 1:<\/strong> When the Side-Length of Square Is Given<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">If the length of one side of the square is known to us, then we can simply calculate the diagonal of a square using the formula $d = a\\sqrt{2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Where, d = length of diagonal of a square and a $=$ side length of the square.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"8-method-2-when-the-perimeter-of-square-is-given\"><strong>Method 2: <\/strong>When the Perimeter of Square Is Given<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">If the perimeter of a square is given or known to us, then follow the below steps<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">First find the side length (a) of the square by using the perimeter of the square formula.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Perimeter of a square$ = 4\\times a$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Side of the square $= \\frac{Perimeter}{4}$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Calculate the diagonal of the square using the formula: $d = a\\sqrt{2}$<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"9-method-3-when-the-area-of-a-square-is-given\"><strong>Method 3: <\/strong>When the Area of a Square Is Given<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">If the area of a square is given or known to us, then follow the below steps:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">First find the side length (a) of the square by using the area of square formula.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Area of a square $= a^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Side of the square $= \\sqrt{Area} = a$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Calculate the diagonal of the square using the formula $d = a\\sqrt{2}$.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-facts-about-diagonals-of-a-square\">Facts about Diagonals of a Square<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The diagonal of a square is longer than its side.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">A square has four lines of symmetry, one vertical, one horizontal, and two diagonal lines.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned about the diagonal of a square formula, its properties, formula, derivation, different methods to calculate the length of a diagonal if the side length is given, and related facts, examples, and practice problems based on the same.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-solved-examples-on-diagonals-of-a-square\">Solved Examples on Diagonals of a Square<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>&nbsp;Find the diagonal length of a square with 18 inches of side.<\/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 side length of the square \u201ca\u201d $= 18$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">According to the diagonal of square formula,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The diagonal length \u201cd\u201d of the square $= a\\sqrt{2} = 18\\times\\sqrt{2} = 18\\times1.414 = 25.42$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the diagonal length of the square is 25.42 inches.<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>The length of the diagonal of a square is <\/strong>$15\\sqrt{2}$<strong> inches. Find the side length of its side.<\/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 diagonal length of the square $= d = 15\\sqrt{2}$<strong> <\/strong>inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us consider the side length of the square to be \u201ca.\u201d<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The diagonal length \u201cd\u201d of the square $= a\\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$15\\times\\sqrt{2} = a\\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Comparing both sides, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a = 15$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the side length of the square is 15 inches.<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the diagonal length of a square field with a perimeter of 124 feet.<\/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 perimeter of the square $= 124$ feet<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us consider the side length of the carrom board to be \u201ca.\u201d<\/p>\n\n\n\n<p class=\"eplus-wrapper\">As we know, the perimeter of the square $= 4a$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$124 = 4a$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a = \\frac{124}{4} = 31$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, $a = 31$ feet<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Diagonal length $= d = a\\sqrt{2} = 31\\times\\sqrt{2} = 43.83$ feet.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the diagonal length of the square field is 43.83 feet.<\/p>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the length of the diagonal of a craft paper if its area is 196 square units.<\/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 Area of the craft paper $= 196$ square units<\/p>\n\n\n\n<p class=\"eplus-wrapper\">As we know craft paper is in the shape of a square.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of a square $= a^2 = 196$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Side length $= a = \\sqrt{196} = 14$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The diagonal length of the square $= d = a\\sqrt{2} = 14\\times\\sqrt{2} = 19.8$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the length of the diagonal of the craft paper is 19.8 units.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-practice-problems-on-diagonals-of-a-square\">Practice Problems on Diagonals of a Square<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Diagonal of a Square - Definition, Formula, Properties, Examples<\/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\">Which of the following objects do not come in a square shape?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Chess board<\/div><div class=\"spq_answer_block\" data-value=\"1\">Floor tiles<\/div><div class=\"spq_answer_block\" data-value=\"2\">Pizza box<\/div><div class=\"spq_answer_block\" data-value=\"3\">Yoga mat<\/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: Yoga mat<br\/>Chess boards, floor tiles, and pizza boxes come in square shape but a yoga mat does not have the shape of a square.<\/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\">What is the total number of diagonals in a square?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">3<\/div><div class=\"spq_answer_block\" data-value=\"3\">4<\/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<br\/>Total number of diagonals in a square is 2.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">When the diagonals of a square bisect each other at a ____ angle.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$90^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$60^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$45^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$30^\\circ$<\/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: $90^\\circ$<br\/>The diagonals of a square bisect each other at a right angle, $90^\\circ$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The length of the diagonal of a square field is  $12\\sqrt{2}$ feet. What is the length of its sides?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">6 feet<\/div><div class=\"spq_answer_block\" data-value=\"1\">8 feet<\/div><div class=\"spq_answer_block\" data-value=\"2\">12 feet<\/div><div class=\"spq_answer_block\" data-value=\"3\">18 feet<\/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: 12 feet<br\/>The length of the diagonal of a square field $= a\\sqrt{2} = 12\\sqrt{2} \\Rightarrow a = 12$.<br>\r\nHence, the length of its side $= 12$ feet.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">What is the length of each diagonal in a square with a side length of 5 inches?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$2\\sqrt{2}$ inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">$2\\sqrt{5}$ inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">$10\\sqrt{2}$ inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">$5\\sqrt{2}$ inches<\/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: $5\\sqrt{2}$ inches<br\/>The length of the diagonal of a square field $= a\\sqrt{2} = 5\\sqrt{2}$<br>\r\nHence, the length of each diagonal in a square with a side length of 5 inches $= 5\\sqrt{2}$ inches.<\/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        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                   \"text\": \"When the diagonals of a square bisect each other at a ____ angle.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The diagonals of a square bisect each other at a right angle, $$90^\\\\circ$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$60^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of a square bisect each other at a right angle, $$90^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$45^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of a square bisect each other at a right angle, $$90^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$30^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diagonals of a square bisect each other at a right angle, $$90^\\\\circ$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$90^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The diagonals of a square bisect each other at a right angle, $$90^\\\\circ$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The diagonals of a square bisect each other at a right angle, $$90^\\\\circ$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The length of the diagonal of a square field is  $$12\\\\sqrt{2}$$ feet. What is the length of its sides?\",\n                    \"text\": \"The length of the diagonal of a square field is  $$12\\\\sqrt{2}$$ feet. What is the length of its sides?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 12\\\\sqrt{2} \\\\Rightarrow a = 12$$.<br>\r\nHence, the length of its side $$= 12$$ feet.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6 feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 12\\\\sqrt{2} \\\\Rightarrow a = 12$$.<br>\r\nHence, the length of its side $$= 12$$ feet.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8 feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 12\\\\sqrt{2} \\\\Rightarrow a = 12$$.<br>\r\nHence, the length of its side $$= 12$$ feet.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"18 feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 12\\\\sqrt{2} \\\\Rightarrow a = 12$$.<br>\r\nHence, the length of its side $$= 12$$ feet.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"12 feet\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 12\\\\sqrt{2} \\\\Rightarrow a = 12$$.<br>\r\nHence, the length of its side $$= 12$$ feet.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 12\\\\sqrt{2} \\\\Rightarrow a = 12$$.<br>\r\nHence, the length of its side $$= 12$$ feet.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the length of each diagonal in a square with a side length of 5 inches?\",\n                    \"text\": \"What is the length of each diagonal in a square with a side length of 5 inches?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 5\\\\sqrt{2}$$<br>\r\nHence, the length of each diagonal in a square with a side length of 5 inches $$= 5\\\\sqrt{2}$$ inches.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2\\\\sqrt{2}$$ inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 5\\\\sqrt{2}$$<br>\r\nHence, the length of each diagonal in a square with a side length of 5 inches $$= 5\\\\sqrt{2}$$ inches.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2\\\\sqrt{5}$$ inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 5\\\\sqrt{2}$$<br>\r\nHence, the length of each diagonal in a square with a side length of 5 inches $$= 5\\\\sqrt{2}$$ inches.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$10\\\\sqrt{2}$$ inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 5\\\\sqrt{2}$$<br>\r\nHence, the length of each diagonal in a square with a side length of 5 inches $$= 5\\\\sqrt{2}$$ inches.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$5\\\\sqrt{2}$$ inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 5\\\\sqrt{2}$$<br>\r\nHence, the length of each diagonal in a square with a side length of 5 inches $$= 5\\\\sqrt{2}$$ inches.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The length of the diagonal of a square field $$= a\\\\sqrt{2} = 5\\\\sqrt{2}$$<br>\r\nHence, the length of each diagonal in a square with a side length of 5 inches $$= 5\\\\sqrt{2}$$ inches.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"14-frequently-asked-questions-on-diagonals-of-a-square\">Frequently Asked Questions on Diagonals of a Square<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-d9428532-be1d-43cd-b944-6af8206c54aa\" 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-d9428532-be1d-43cd-b944-6af8206c54aa\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d9428532-be1d-43cd-b944-6af8206c54aa\"><strong>Is the side of a square and its diagonal the same length?<\/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-d9428532-be1d-43cd-b944-6af8206c54aa\">\n\n<p class=\"eplus-wrapper\">No, the side of a square and its diagonal aren\u2019t of the same length. The diagonal of a square is greater in length than its side.<\/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-d9428532-be1d-43cd-b944-6af8206c54aa\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d9428532-be1d-43cd-b944-6af8206c54aa\"><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-1-d9428532-be1d-43cd-b944-6af8206c54aa\">\n\n<p class=\"eplus-wrapper\">The quadrilaterals having diagonals that bisect each other: a rectangle, square, parallelogram, and rhombus.<\/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-d9428532-be1d-43cd-b944-6af8206c54aa\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d9428532-be1d-43cd-b944-6af8206c54aa\"><strong>How to calculate the diagonal of a square when its side is given?<\/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-d9428532-be1d-43cd-b944-6af8206c54aa\">\n\n<p class=\"eplus-wrapper\">If the length of side of the square is given, then we can calculate the diagonal of a square using the formula $d = side\\times\\sqrt{2}$.<\/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-3-d9428532-be1d-43cd-b944-6af8206c54aa\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d9428532-be1d-43cd-b944-6af8206c54aa\"><strong>How to find the length of the diagonal of a square when its perimeter is given?<\/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-3-d9428532-be1d-43cd-b944-6af8206c54aa\">\n\n<p class=\"eplus-wrapper\">If the perimeter of the square is given then first calculate the side length using the formula&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">\u201ca\u201d $= \\frac{perimeter}{4}$ , then substitute the value of \u201ca\u201d in the diagonal length of a square formula $d = a\\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow d = \\bigg(\\frac{perimeter}{4}\\bigg)\\sqrt{2}$<\/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-4-d9428532-be1d-43cd-b944-6af8206c54aa\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d9428532-be1d-43cd-b944-6af8206c54aa\"><strong>How to find the length of the diagonal of a square when its area is given?<\/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-4-d9428532-be1d-43cd-b944-6af8206c54aa\">\n\n<p class=\"eplus-wrapper\">If the area of the square is given then first calculate the side length using the formula&nbsp;\u201ca\u201d $= \\sqrt{Area}$ then substitute the value of \u201ca\u201d in the diagonal length of a square formula $d = a\\sqrt{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow d = \\sqrt{Area}\\times\\sqrt{2}$.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Diagonal of a Square? Diagonals of a square are the line segments joining opposite vertices. A flat, closed shape with four equal sides, four vertices (like craft paper, a photo frame), and four right angles is known as a square. Take a look at the square craft paper shown below. Let\u2019s connect &#8230; <a title=\"Diagonal of a Square &#8211; Definition, Formula, Properties, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/diagonal-of-a-square\" aria-label=\"More on Diagonal of a Square &#8211; Definition, Formula, Properties, 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-27377","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\/27377","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=27377"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27377\/revisions"}],"predecessor-version":[{"id":39959,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27377\/revisions\/39959"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=27377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=27377"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=27377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}