{"id":30522,"date":"2023-06-14T10:36:07","date_gmt":"2023-06-14T10:36:07","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?p=30522"},"modified":"2023-11-15T18:10:46","modified_gmt":"2023-11-15T18:10:46","slug":"perimeter-of-rhombus","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/perimeter-of-rhombus","title":{"rendered":"Perimeter of a Rhombus &#8211; Definition, Formula, Examples, Facts, FAQs"},"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-aba3cae9-3977-4ec1-aaa7-d711a7a6cc57\" 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\/perimeter-of-rhombus#0-perimeter-of-a-rhombus-formulas>Perimeter of a Rhombus: Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perimeter-of-rhombus#1-how-to-find-the-perimeter-of-a-rhombus>How to Find the Perimeter of a Rhombus<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perimeter-of-rhombus#4-perimeter-of-a-rhombus-using-one-diagonal-and-one-angle>Perimeter of a Rhombus Using One Diagonal and One Angle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perimeter-of-rhombus#6-solved-examples-on-the-perimeter-of-a-rhombus>Solved Examples on the Perimeter of a Rhombus<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perimeter-of-rhombus#7-practice-problems-on-perimeter-of-a-rhombus>Practice Problems on Perimeter of a Rhombus<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/perimeter-of-rhombus#8-frequently-asked-questions-on-perimeter-of-a-rhombus>Frequently Asked Questions on Perimeter of a Rhombus<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<p><strong>The perimeter of a rhombus is the total length of its outer boundary. It is measured in linear units, such as <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/foot\"><strong>feet<\/strong><\/a><strong>, <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/inch\"><strong>inches<\/strong><\/a><strong>, yards, etc.<\/strong><\/p>\n\n\n\n<p>Perimeter of a rhombus $= 4 \\times side$<\/p>\n\n\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/rhombus\">rhombus<\/a> is a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/quadrilateral\">quadrilateral<\/a> (a four-sided <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polygon\">polygon<\/a>) with the following properties:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>All sides are equal.<\/li>\n\n\n\n<li>Opposite angles are congruent.<\/li>\n\n\n\n<li>Adjacent angles are supplementary.<\/li>\n\n\n\n<li>Opposite sides are parallel.<\/li>\n\n\n\n<li>The altitude is a distance at right angles between two parallel sides.<\/li>\n\n\n\n<li>The diagonals of a rhombus bisect each other at the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-angle\">right angles<\/a>.<\/li>\n\n\n\n<li>Each diagonal bisects the vertex angle.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>Its properties make it a unique and important geometric shape. Let\u2019s explore the perimeter of rhombus in detail.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"340\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rhombus-ABCD.png\" alt=\"Rhombus ABCD\" class=\"wp-image-35985\" title=\"Rhombus ABCD\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rhombus-ABCD.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rhombus-ABCD-300x165.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>The image above shows a rhombus ABCD, along with its important properties.<\/p>\n\n\n\n<p>So, what is the perimeter of the rhombus ABCD? <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/perimeter\">How do you find the perimeter<\/a> of a rhombus? Let\u2019s discuss formulas and methods in detail.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"0-perimeter-of-a-rhombus-formulas\">Perimeter of a Rhombus: Formulas<\/h2>\n\n\n\n<p>Let\u2019s discuss the formulas for the perimeter of a rhombus with two cases.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When the side length is known<\/li>\n<\/ul>\n\n\n\n<p>Perimeter of a rhombus with side \u201ca\u201d $= 4 \\times a$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When the length of the diagonals is known<\/li>\n<\/ul>\n\n\n\n<p>Perimeter of a rhombus with diagonals p and $q = 2\\sqrt{p^{2} + q^{2}}$<\/p>\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\/determine-the-perimeter\" 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_with_missing_side_2_pt.png\" alt=\"Determine the Perimeter 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\">Determine the Perimeter 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\/determine-the-perimeter-of-regular-shapes\" 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_with_missing_side_1_pt.png\" alt=\"Determine the Perimeter of Regular Shapes 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\">Determine the Perimeter of Regular Shapes 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-perimeter-of-irregular-shapes\" 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_monsters_in_city_6_gm.png\" alt=\"Find Perimeter of Irregular Shapes 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 Perimeter of Irregular Shapes 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-perimeter-of-regular-shapes\" 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_monsters_in_city_7_gm.png\" alt=\"Find Perimeter of Regular Shapes 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 Perimeter of Regular Shapes 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-perimeter-using-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_monsters_in_city_5_gm.png\" alt=\"Find Perimeter using 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\">Find Perimeter using 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\/find-the-perimeter-of-irregular-shapes\" 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_irregular_pt.png\" alt=\"Find the Perimeter of Irregular Shapes 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 Irregular Shapes 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-polygons\" 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_1_pt.png\" alt=\"FInd the Perimeter of Polygons 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 Polygons 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-regular-shapes\" 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_regular_pt.png\" alt=\"Find the Perimeter of Regular Shapes 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 Regular Shapes 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-quadrilaterals\" 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_3_pt.png\" alt=\"Find the Perimeter of the Quadrilaterals 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 Quadrilaterals 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-shapes-using-grids\" 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_length_pt.png\" alt=\"Find the Perimeter of the Shapes Using Grids 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 Shapes Using Grids 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 = 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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\" id=\"1-how-to-find-the-perimeter-of-a-rhombus\">How to Find the Perimeter of a Rhombus<\/h2>\n\n\n\n<p>To find the perimeter of a rhombus, first note down the known dimensions. Make sure that all the measurements are in the same unit.<\/p>\n\n\n\n<p>If the side length of a rhombus is known, use the first formula $P = 4\\times$<strong> side length<\/strong>.&nbsp;<\/p>\n\n\n\n<p>If the lengths of the two diagonals of a rhombus are known $(say\\; d_{1}$ and $d_{2})$, use the formula $= 2\\sqrt{d_{1}^{2} + d_{2}^{2}}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-perimeter-of-a-rhombus-using-the-side-lengths\">Perimeter of a Rhombus Using the Side Lengths<\/h2>\n\n\n\n<p>The perimeter of a rhombus is defined as the total distance around the outline of the shape. It is the sum of the lengths of all four sides. Since all sides of a rhombus are equal, the formula for the perimeter is simply four times the length of one side.<\/p>\n\n\n\n<p>Perimeter of a rhombus with side \u201cx\u201d $= x + x + x + x$<\/p>\n\n\n\n<p><strong>Perimeter <\/strong>$= 4\\times $ <strong>Side Length <\/strong>$= 4x$<\/p>\n\n\n\n<p><strong>Example: Find the perimeter of a rhombus with a side length of 8 inches.<\/strong><\/p>\n\n\n\n<p>Perimeter $= 4\\times$ Side Length<\/p>\n\n\n\n<p>Perimeter $= 4 \\times 8$ inches<\/p>\n\n\n\n<p>Perimeter $= 32$ inches<\/p>\n\n\n\n<p>So, the perimeter of the rhombus is 32 inches.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-perimeter-of-a-rhombus-using-diagonals\">Perimeter of a Rhombus Using Diagonals<\/h2>\n\n\n\n<p>When the length of the diagonals of a rhombus is given, we first find the side length of the rhombus using the Pythagoras\u2019 theorem.&nbsp;<\/p>\n\n\n\n<p>The properties of rhombus we use here are&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A rhombus is divided into 4 congruent right triangles by its two diagonals.<\/li>\n\n\n\n<li>The diagonals bisect each other at right angles.<\/li>\n<\/ul>\n\n\n\n<p>Let us consider a rhombus ABCD with diagonals p and q and with side length \u201ca.\u201d<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"315\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/formula-for-perimeter-of-rhombus-ABCD-with-diagonals-p-and-q.png\" alt=\"Formula for perimeter of rhombus ABCD with diagonals p and q\" class=\"wp-image-35986\" title=\"Formula for perimeter of rhombus ABCD with diagonals p and q\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/formula-for-perimeter-of-rhombus-ABCD-with-diagonals-p-and-q.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/formula-for-perimeter-of-rhombus-ABCD-with-diagonals-p-and-q-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Consider the triangle AOD.&nbsp;<\/p>\n\n\n\n<p>Since the diagonals bisect at right angles, we can write&nbsp;<\/p>\n\n\n\n<p>AO $= \\frac{p}{2}$ and OD $= \\frac{q}{2}$.&nbsp;<\/p>\n\n\n\n<p>On applying the Pythagoras\u2019 theorem for triangle AOD, we get<\/p>\n\n\n\n<p>$a^{2} = \\frac{p^{2}}{4} + \\frac{q^{2}}{4}$<\/p>\n\n\n\n<p>$a = \\sqrt{\\frac{p^{2} + q{2}}{2}}$<\/p>\n\n\n\n<p>Perimeter of a rhombus $= 4a =4 \\times \\sqrt{\\frac{p^{2} + q^{2}}{2}} = 2\\sqrt{p^{2} + q^{2}}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-perimeter-of-a-rhombus-using-one-diagonal-and-one-angle\">Perimeter of a Rhombus Using One Diagonal and One Angle<\/h2>\n\n\n\n<p>Suppose that you know the length of one of the two diagonals and one <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles\">interior angle<\/a>. Now, to find the perimeter of the rhombus, you first need to find the length of the side using the different properties of a rhombus. Let\u2019s understand this with an example.&nbsp;<\/p>\n\n\n\n<p><strong>Example: Find the perimeter of the rhombus ABCD given below.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"665\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rhombus-ABCD-with-one-diagonal-and-one-angle.png\" alt=\"Rhombus ABCD with one diagonal and one angle\" class=\"wp-image-35987\" title=\"Rhombus ABCD with one diagonal and one angle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rhombus-ABCD-with-one-diagonal-and-one-angle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rhombus-ABCD-with-one-diagonal-and-one-angle-280x300.png 280w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Given:<\/strong> $\\angle A = 60^{\\circ}$ and $AC = 20$<\/p>\n\n\n\n<p>Each diagonal bisects the vertex angle.&nbsp;<\/p>\n\n\n\n<p>Thus, $\\angle BAE = \\frac{1}{2} \\angle BAD = 30^{\\circ}$<\/p>\n\n\n\n<p>The diagonals of a rhombus bisect each other at right angles.<\/p>\n\n\n\n<p>Thus, $\\angle AEB = 90^{\\circ}$ and $AE = \\frac{1}{2}\\times AC = 10$<\/p>\n\n\n\n<p>In triangle AEB, $cos(\\angle BAE) = cos(30^{\\circ})= \\frac{\\sqrt{3}}{2}$<\/p>\n\n\n\n<p>Also, $cos(\\angle BAE) = \\frac{AE}{AB}$<\/p>\n\n\n\n<p>Thus,&nbsp; $\\frac{\\sqrt{3}}{2} = \\frac{10}{AB}$<\/p>\n\n\n\n<p>$AB = \\frac{20}{\\sqrt{3}}$ \u2026side of rhombus ABCD<\/p>\n\n\n\n<p>Thus, perimeter of rhombus $ABCD = 4 \\times side = 4 \\times \\frac{20}{\\sqrt{3}} = \\frac{80}{\\sqrt{3}} \\approx 46$ units<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned how to find the perimeter of a rhombus and also the different methods to calculate the perimeter of a rhombus. Let\u2019s use these concepts and move ahead to solve a few examples and practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-solved-examples-on-the-perimeter-of-a-rhombus\">Solved Examples on the Perimeter of a Rhombus<\/h2>\n\n\n\n<p><strong>1. What is the perimeter of a rhombus with each side length equal to 10 inches?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>Side of rhombus $= a = 10$ inches<\/p>\n\n\n\n<p>Perimeter of rhombus $= 4a = 4 \\times&nbsp; 8 = 32$ inches<\/p>\n\n\n\n<p><strong>2. Find the side of a rhombus if the perimeter is 36 feet.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;&nbsp;<\/p>\n\n\n\n<p>Perimeter of a rhombus $= 36$ feet<\/p>\n\n\n\n<p>Let the side of the rhombus be \u201ca\u201d feet.<\/p>\n\n\n\n<p>$4a = 36$ feet<\/p>\n\n\n\n<p>$a = \\frac{36}{4} = 9$ feet<\/p>\n\n\n\n<p><strong>3. If the diagonals of the rhombus are <\/strong><strong>6<\/strong><strong> and <\/strong><strong>8<\/strong><strong> inches, then what is the perimeter of the rhombus?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;&nbsp;<\/p>\n\n\n\n<p>Let $p = 6$ inches and $q = 8$ inches<\/p>\n\n\n\n<p>Perimeter of a rhombus with diagonals p and $q = 2\\sqrt{p^{2} + q^{2}}$<\/p>\n\n\n\n<p>Perimeter of the rhombus $= 2\\sqrt{6^{2} + 8^{2}}$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=2 \\times 10$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=20$ inches<\/p>\n\n\n\n<p><strong>4. ABCD is a rhombus with sides 15 inches. What is the perimeter of the rhombus ABCD?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;&nbsp;<\/p>\n\n\n\n<p>Side of rhombus $= a = 15$ inches<\/p>\n\n\n\n<p>Perimeter of rhombus $= 4a = 4 \\times 15 = 60$ inches<\/p>\n\n\n\n<p><strong>5. A field is in the shape of a rhombus with sides 13 feet. Find the length of the boundary of the field.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>Length of the boundary of the field = Perimeter of the rhombus<\/p>\n\n\n\n<p>Side of rhombus shaped field $= a = 13$ feet<\/p>\n\n\n\n<p>Perimeter of the field $= 4a = 4 \\times 13 = 42$ feet<\/p>\n\n\n\n<p>Length of the boundary of the field $= 42$ feet<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-practice-problems-on-perimeter-of-a-rhombus\">Practice Problems on Perimeter of a Rhombus<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Perimeter of a Rhombus - Definition, Formula, Examples, Facts, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">If the perimeter of a rhombus is 48 in, then what is the length of each side?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">3 inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">10 inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">12 inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">16 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: 12 inches<br\/>Perimeter of a rhombus$= 48$ inches<br>\r\nLet the side of the rhombus be \u201ca\u201d inches.<br>\r\n$4a = 48$<br>\r\n$a = \\frac{48}{4} = 12$ inches<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the perimeter of the square if the side length is 18 feet?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">36 feet<\/div><div class=\"spq_answer_block\" data-value=\"1\">52 feet<\/div><div class=\"spq_answer_block\" data-value=\"2\">64 feet<\/div><div class=\"spq_answer_block\" data-value=\"3\">72 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: 72 feet<br\/>side of rhombus, i.e., $a = 18$ feet<br>\r\nPerimeter of rhombus $= 4a = 4 \\times 18 = 72$ feet<\/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\">The formula for the perimeter of a rhombus with side \u201ca\u201d is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2a<\/div><div class=\"spq_answer_block\" data-value=\"1\">4a<\/div><div class=\"spq_answer_block\" data-value=\"2\">5a<\/div><div class=\"spq_answer_block\" data-value=\"3\">6a<\/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: 4a<br\/>Perimeter of rhombus with side \u201ca\u201d $= 4a$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">If the diagonals of the rhombus are 21 inches and 20 inches, then what will be the perimeter of the rhombus?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">58 inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">$58\\sqrt{2}$ inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">84 inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">164 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: 58 inches<br\/>Perimeter of the rhombus $= 2\\sqrt{p^{2} + q^{2}} =2\\sqrt{21^{2} + 20^{2}} = 2\\sqrt{841} = 2 \\times 29 = 58$ in<\/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\">If the perimeter of a rhombus is 68 inches and the length of one diagonal is 16 inches, then what is the length of the other diagonal?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">12 inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">18 inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">27 inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">30 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: 30 inches<br\/>Perimeter of the rhombus $= 2\\sqrt{p^{2} + q^{2}}$<br>\r\nLet $p = 16$ inches<br>\r\n$68 = 2\\sqrt{p^{2} + q^{2}}$<br>\r\n$34 = \\sqrt{16^{2} + q^{2}}$<br>\r\n$1156 = 256 + q^{2}$<br>\r\n$q^{2} = 1156\\;-\\;256 = 900$<br>\r\n$q = 30$ 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        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": 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\"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of a rhombus$$= 48$$ inches<br>\r\nLet the side of the rhombus be \u201ca\u201d inches.<br>\r\n$$4a = 48$$<br>\r\n$$a = \\\\frac{48}{4} = 12$$ inches\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"16 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of a rhombus$$= 48$$ inches<br>\r\nLet the side of the rhombus be \u201ca\u201d inches.<br>\r\n$$4a = 48$$<br>\r\n$$a = \\\\frac{48}{4} = 12$$ inches\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"12 inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Perimeter of a rhombus$$= 48$$ inches<br>\r\nLet the side of the rhombus be \u201ca\u201d inches.<br>\r\n$$4a = 48$$<br>\r\n$$a = \\\\frac{48}{4} = 12$$ inches\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Perimeter of a rhombus$$= 48$$ inches<br>\r\nLet the side of the rhombus be \u201ca\u201d inches.<br>\r\n$$4a = 48$$<br>\r\n$$a = \\\\frac{48}{4} = 12$$ inches\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the perimeter of the square if the side length is 18 feet?\",\n                    \"text\": \"What is the perimeter of the square if the side length is 18 feet?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"side of rhombus, i.e., $$a = 18$$ feet<br>\r\nPerimeter of rhombus $$= 4a = 4 \\\\times 18 = 72$$ feet\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"36 feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"side of rhombus, i.e., $$a = 18$$ feet<br>\r\nPerimeter of rhombus $$= 4a = 4 \\\\times 18 = 72$$ feet\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"52 feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"side of rhombus, i.e., $$a = 18$$ feet<br>\r\nPerimeter of rhombus $$= 4a = 4 \\\\times 18 = 72$$ feet\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"64 feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"side of rhombus, i.e., $$a = 18$$ feet<br>\r\nPerimeter of rhombus $$= 4a = 4 \\\\times 18 = 72$$ feet\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"72 feet\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"side of rhombus, i.e., $$a = 18$$ feet<br>\r\nPerimeter of rhombus $$= 4a = 4 \\\\times 18 = 72$$ feet\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"side of rhombus, i.e., $$a = 18$$ feet<br>\r\nPerimeter of rhombus $$= 4a = 4 \\\\times 18 = 72$$ feet\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The formula for the perimeter of a rhombus with side \u201ca\u201d is\",\n                    \"text\": \"The formula for the perimeter of a rhombus with side \u201ca\u201d is\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Perimeter of rhombus with side \u201ca\u201d $$= 4a$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2a\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of rhombus with side \u201ca\u201d $$= 4a$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5a\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of rhombus with side \u201ca\u201d $$= 4a$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6a\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of rhombus with side \u201ca\u201d $$= 4a$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"4a\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Perimeter of rhombus with side \u201ca\u201d $$= 4a$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Perimeter of rhombus with side \u201ca\u201d $$= 4a$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the diagonals of the rhombus are 21 inches and 20 inches, then what will be the perimeter of the rhombus?\",\n                    \"text\": \"If the diagonals of the rhombus are 21 inches and 20 inches, then what will be the perimeter of the rhombus?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}} =2\\\\sqrt{21^{2} + 20^{2}} = 2\\\\sqrt{841} = 2 \\\\times 29 = 58$$ in\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$58\\\\sqrt{2}$$ inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}} =2\\\\sqrt{21^{2} + 20^{2}} = 2\\\\sqrt{841} = 2 \\\\times 29 = 58$$ in\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"84 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}} =2\\\\sqrt{21^{2} + 20^{2}} = 2\\\\sqrt{841} = 2 \\\\times 29 = 58$$ in\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"164 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}} =2\\\\sqrt{21^{2} + 20^{2}} = 2\\\\sqrt{841} = 2 \\\\times 29 = 58$$ in\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"58 inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}} =2\\\\sqrt{21^{2} + 20^{2}} = 2\\\\sqrt{841} = 2 \\\\times 29 = 58$$ in\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}} =2\\\\sqrt{21^{2} + 20^{2}} = 2\\\\sqrt{841} = 2 \\\\times 29 = 58$$ in\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the perimeter of a rhombus is 68 inches and the length of one diagonal is 16 inches, then what is the length of the other diagonal?\",\n                    \"text\": \"If the perimeter of a rhombus is 68 inches and the length of one diagonal is 16 inches, then what is the length of the other diagonal?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\nLet $$p = 16$$ inches<br>\r\n$$68 = 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\n$$34 = \\\\sqrt{16^{2} + q^{2}}$$<br>\r\n$$1156 = 256 + q^{2}$$<br>\r\n$$q^{2} = 1156\\\\;-\\\\;256 = 900$$<br>\r\n$$q = 30$$ inches\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\nLet $$p = 16$$ inches<br>\r\n$$68 = 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\n$$34 = \\\\sqrt{16^{2} + q^{2}}$$<br>\r\n$$1156 = 256 + q^{2}$$<br>\r\n$$q^{2} = 1156\\\\;-\\\\;256 = 900$$<br>\r\n$$q = 30$$ inches\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"18 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\nLet $$p = 16$$ inches<br>\r\n$$68 = 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\n$$34 = \\\\sqrt{16^{2} + q^{2}}$$<br>\r\n$$1156 = 256 + q^{2}$$<br>\r\n$$q^{2} = 1156\\\\;-\\\\;256 = 900$$<br>\r\n$$q = 30$$ inches\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"27 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\nLet $$p = 16$$ inches<br>\r\n$$68 = 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\n$$34 = \\\\sqrt{16^{2} + q^{2}}$$<br>\r\n$$1156 = 256 + q^{2}$$<br>\r\n$$q^{2} = 1156\\\\;-\\\\;256 = 900$$<br>\r\n$$q = 30$$ inches\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"30 inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\nLet $$p = 16$$ inches<br>\r\n$$68 = 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\n$$34 = \\\\sqrt{16^{2} + q^{2}}$$<br>\r\n$$1156 = 256 + q^{2}$$<br>\r\n$$q^{2} = 1156\\\\;-\\\\;256 = 900$$<br>\r\n$$q = 30$$ inches\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Perimeter of the rhombus $$= 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\nLet $$p = 16$$ inches<br>\r\n$$68 = 2\\\\sqrt{p^{2} + q^{2}}$$<br>\r\n$$34 = \\\\sqrt{16^{2} + q^{2}}$$<br>\r\n$$1156 = 256 + q^{2}$$<br>\r\n$$q^{2} = 1156\\\\;-\\\\;256 = 900$$<br>\r\n$$q = 30$$ inches\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-frequently-asked-questions-on-perimeter-of-a-rhombus\">Frequently Asked Questions on Perimeter of a Rhombus<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\" 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-0-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\"><strong>What is the difference between area and perimeter?<\/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-0-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\">\n\n<p>The area of a 2D shape is the region bounded by the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/shape\">shape<\/a>, whereas the perimeter is the length of the boundary of the shape.<\/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-1-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\"><strong>What is the perimeter of the square?<\/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-1-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\">\n\n<p><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/perimeter-of-a-square\">Perimeter of a square<\/a> $=&nbsp; 4 \\times$ side of the square<\/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-2-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\"><strong>What is the area of a rhombus?<\/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-2-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\">\n\n<p>Area of rhombus when diagonals are given $= \\frac{1}{2} \\times d_{1} \\times d_{2}$<\/p>\n\n\n\n<p>Area of rhombus when base and height is given $= b \\times h$<\/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-3-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\"><strong>Are all rhombuses squares?<\/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-3-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\">\n\n<p>All squares are rhombuses, but all rhombuses are not squares. If you have a rhombus with four equal interior angles, you have a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/square\">square<\/a>. A square is a special case of a rhombus, because it has four equal-length sides and goes above and beyond that to also have four right angles.<\/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-4-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\"><strong>Are all four angles of a rhombus equal?<\/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-4-7eb10ff2-a8ff-4e6c-9546-a6e43a50df6e\">\n\n<p>No, the opposite angles of a rhombus are equal and the adjacent angles are supplementary.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>The perimeter of a rhombus is the total length of its outer boundary. It is measured in linear units, such as feet, inches, yards, etc. Perimeter of a rhombus $= 4 \\times side$ A rhombus is a quadrilateral (a four-sided polygon) with the following properties: Its properties make it a unique and important geometric shape. &#8230; <a title=\"Perimeter of a Rhombus &#8211; Definition, Formula, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/perimeter-of-rhombus\" aria-label=\"More on Perimeter of a Rhombus &#8211; Definition, Formula, Examples, Facts, FAQs\">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-30522","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\/30522","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=30522"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/30522\/revisions"}],"predecessor-version":[{"id":35988,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/30522\/revisions\/35988"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=30522"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=30522"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=30522"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}