{"id":33996,"date":"2023-09-08T17:23:00","date_gmt":"2023-09-08T17:23:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=33996"},"modified":"2023-09-12T07:11:18","modified_gmt":"2023-09-12T07:11:18","slug":"area-of-parallelogram-formula-vector-form-facts-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-parallelogram","title":{"rendered":"Area of Parallelogram &#8211; Formula, Vector Form, Facts, Examples, 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-41f827f8-f4cc-4117-b666-bf6a87fa56cc\" 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\/area-of-parallelogram#0-what-is-the-area-of-parallelogram>What Is the Area of Parallelogram?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-parallelogram#2-how-to-find-the-area-of-a-parallelogram>How to Find the Area of a Parallelogram<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-parallelogram#3-area-of-parallelogram-list-of-formulas>Area of Parallelogram: List of Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-parallelogram#6-solved-examples-on-the-area-of-parallelogram>Solved Examples on the Area of Parallelogram<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-parallelogram#7-practice-problems-on-the-area-of-parallelogram>Practice Problems on the Area of Parallelogram<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-parallelogram#8-frequently-asked-questions-on-the-area-of-parallelogram>Frequently Asked Questions on the Area of Parallelogram<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-area-of-parallelogram\">What Is the Area of Parallelogram?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The area of a parallelogram is defined as the measure of the two-dimensional space enclosed within its boundaries. It is calculated by multiplying the length of the base by its height<\/strong>, <strong>which is the perpendicular distance between the base and the opposite side.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallelogram\">parallelogram<\/a> is a special <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/quadrilateral\">quadrilateral<\/a> in which opposite sides are parallel and equal in length.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The given figure shows a parallelogram ABCD.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">AB II CD and AB = CD.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">AD II BC and AD = BC.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"322\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/parallelogram-ABCD.png\" alt=\"Parallelogram ABCD\" class=\"wp-image-34006\" title=\"Parallelogram ABCD\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/parallelogram-ABCD.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/parallelogram-ABCD-300x156.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Area of a parallelogram = Base <\/strong>$\\times$<strong> Height<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You might be wondering if this is the same formula that we use to calculate the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/area-of-rectangle-formula\">area of a rectangle<\/a>. That&#8217;s true!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The formulas for the area of a parallelogram and a rectangle are the same because any parallelogram can be transformed into a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/rectangle\">rectangle<\/a> with the same base and height. Try to visualize it with the help of the given diagram!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"295\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/transforming-a-parallelogram-into-a-rectangle.png\" alt=\"Transforming a parallelogram into a rectangle\" class=\"wp-image-34008\" title=\"Transforming a parallelogram into a rectangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/transforming-a-parallelogram-into-a-rectangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/transforming-a-parallelogram-into-a-rectangle-300x143.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Since the base and height of the parallelogram remain the same in this transformation, the area of the parallelogram is equal to the area of the resulting rectangle.<\/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\/add-to-find-the-area\" 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_find_area_pt.png\" alt=\"Add to Find the Area 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\">Add to Find the Area 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\/area-of-composite-figure\" 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_10_gm.png\" alt=\"Area of Composite Figure 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 of Composite Figure 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 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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\/fractions_real_life_prob_area_pt.png\" alt=\"Area Word Problems on Product of Fractions 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 Word Problems on Product of Fractions 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\/build-the-area\" 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\" 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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 Area of Rectilinear 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-area-by-multiplying-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_multi_side_length_1_pt.png\" alt=\"Find Area by Multiplying 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 Area by Multiplying 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-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-by-multiplying-the-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_multiply_pt.png\" alt=\"Find the Area by Multiplying the 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 the Area by Multiplying the 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-area-of-shapes-using-unit-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_area_unit_square_side_length_pt.png\" alt=\"Find the Area of Shapes Using Unit 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 Area of Shapes Using Unit 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><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 = 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-area-of-parallelogram-formula\">Area of Parallelogram: Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The area of a parallelogram can be calculated using the formula:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td><strong>Area = base <\/strong>$\\times$<strong> height<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"313\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/parallelogram-area-formula.png\" alt=\"Parallelogram area formula\" class=\"wp-image-34009\" title=\"Parallelogram area formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/parallelogram-area-formula.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/parallelogram-area-formula-300x151.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>base<\/strong> refers to the length of base of the parallelogram. We can choose any of the four sides of a parallelogram as the base.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>height<\/strong> is the perpendicular distance between the base and the opposite parallel side. It&#8217;s important to note that the height must be measured perpendicular to the base we choose.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s say the base of the parallelogram is represented by &#8216;<strong>b<\/strong>&#8216; units and the height by &#8216;<strong>h<\/strong>&#8216; units.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The formula for the area of the parallelogram can be written as:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td><strong>Area = <\/strong><strong>b<\/strong><strong> <\/strong>$\\times$ <strong>h<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The area of a parallelogram is expressed in square units. For example, if the base and height are measured in inches, the area will be in square inches $(in^{2})$.<\/p>\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\/add-fractions-using-area-models\" 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\/add-fractions-using-area-models.jpeg\" alt=\"Add Fractions using Area Models 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-like-fractions-using-area-models\" 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\/add-like-fractions-using-area-models.jpeg\" alt=\"Add Like Fractions using Area Models 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-mixed-numbers-and-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" 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src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/compare-fractions-using-area-model.jpeg\" alt=\"Compare Fractions Using Area Model 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-the-area-model\" 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\/complete-the-area-model.jpeg\" alt=\"Complete the Area Model 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 class=\"worksheet-card-container-outer\">\r\n\t<a 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-how-to-find-the-area-of-a-parallelogram\">How to Find the Area of a Parallelogram<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The area of a parallelogram can be calculated in the following cases:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. When the base and height are known.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. When the angle between the adjacent sides and their lengths are known.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3. When the two diagonals and any of the angles at which they intersect are known.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Finding Area of Parallelogram Using Base and Height<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s say the base of the parallelogram is represented by &#8216;<strong>b<\/strong>&#8216; units and the height by &#8216;<strong>h<\/strong>&#8216; units.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The formula for the area of the parallelogram can be written as:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Area = base <\/strong>$\\times$<strong> height<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Area = b <\/strong>$\\times$ <strong>h (square units)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example:<\/strong> In a parallelogram, if the base is 11 units and the height is 6 units, what is the area?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base of the parallelogram = 11 units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Height of the parallelogram = 6 units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area of parallelogram = b $\\times$ h = 11 $\\times$ 6 = 66 square units of 66 $unit^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Finding Area of Parallelogram Using Lengths of Sides<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The area of the parallelogram can also be calculated without height. Let the lengths of adjacent sides be \u2018a\u2019 units and \u2018b\u2019 units, and \u03b8 be the angle between them.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Area of parallelogram = a $<\/strong>\\times$ b $\\times$ sin(\u03b8)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where &#8216;a&#8217; and &#8216;b&#8217; are the lengths of the adjacent sides,&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03b8 is the angle between them.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"515\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/area-of-parallelogram.png\" alt=\"Area of parallelogram\" class=\"wp-image-34010\" title=\"Area of parallelogram\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/area-of-parallelogram.png 600w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/area-of-parallelogram-300x258.png 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">This formula is derived from the fact that a parallelogram can be divided into two congruent triangles. By using the trigonometric relationship between the sides and angles of a triangle, we can calculate the area of each triangle and then sum them up to find the total area of the parallelogram.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: <\/strong>In a parallelogram, the lengths of the adjacent sides are 5 units and 8 units, and the angle between them is 60 degrees. Find the area of the parallelogram.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a = 5 units, b = 8 units, \u03b8 = 60 degrees<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using the formula for the area of a parallelogram with adjacent sides and the angle between them:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = a $\\times$ b $\\times$ sin(\u03b8)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area =\u00a0 5 $\\times$ 8 $\\times$ sin(60\u00ba)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = 40 $\\times \\frac{\\sqrt{3}}{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = $20\\sqrt{3}$ square units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the area of the parallelogram is $20\\sqrt{3}$ square units.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Finding Area of Parallelogram Using Diagonals<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To calculate the area of a parallelogram using the lengths of its diagonals, you can use the following two formulas:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Area = <\/strong>$\\frac{1}{2} \\times d_{1} \\times d_{2} \\times sin(x)$<strong>\u00a0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Area = <\/strong>$\\frac{1}{2} \\times d_{1} \\times d_{2} \\times sin(y)$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>d<sub>1<\/sub><\/strong> and <strong>d<sub>2<\/sub><\/strong> are the lengths of the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/diagonal\">diagonals<\/a> of the parallelogram.<\/li>\n\n\n\n<li>x or y is the angle of intersection between the diagonals.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"537\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/formula-for-area-of-parallelogram-using-diagonals.png\" alt=\"Formula for area of parallelogram using diagonals\" class=\"wp-image-34011\" title=\"Formula for area of parallelogram using diagonals\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/formula-for-area-of-parallelogram-using-diagonals.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/formula-for-area-of-parallelogram-using-diagonals-300x260.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: <\/strong>In a parallelogram, the lengths of the diagonals are 6 units and 8 units, and the angle between the diagonals is 90 degrees. Find the area of the parallelogram.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>d<sub>1<\/sub><\/strong>= 6 units, <strong>d<sub>2<\/sub><\/strong> = 8 units, x = 90 degrees<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using the formula for the area of a parallelogram with the lengths of its diagonals:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = $\\frac{1}{2} \\times d_{1} \\times d_{2} \\times sin(x)$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = $\\frac{1}{2} \\times 6 \\times 8 \\times sin(90)$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area $= \\frac{1}{2} \\times 6 \\times 81 = 24$ square units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the area of the parallelogram is 24 square units<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-area-of-parallelogram-list-of-formulas\">Area of Parallelogram: List of Formulas<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td colspan=\"2\"><strong>Formulas to Calculate Area of a Parallelogram<\/strong><\/td><\/tr><tr><td>Using Base and Height<\/td><td>A = b \u00d7 h<\/td><\/tr><tr><td>Using Sides<\/td><td>A = a \u00d7 b \u00d7 sin(x)<\/td><\/tr><tr><td>Using Diagonals<\/td><td>A = $\\frac{1}{2}$ \u00d7 d1 \u00d7 d2 \u00d7 sin(y)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-facts-about-area-of-a-parallelogram\">Facts about Area of a Parallelogram<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The area of a parallelogram is equal to the area of a triangle with the same base and height.<\/li>\n\n\n\n<li>In a parallelogram, opposite sides are parallel and equal. This means that you can use any side as the base and the corresponding height to calculate the area.<\/li>\n\n\n\n<li>Any parallelogram can be transformed into a rectangle with the same base and height. The area of the parallelogram remains unchanged during this transformation, which explains why the area formula for a parallelogram is the same as that for a rectangle.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we have learned about the area of parallelogram.the area of a parallelogram is necessary for measurements, real-world applications, problem-solving, understanding geometric relationships, and as a stepping stone for further mathematical and professional pursuits. Let&#8217;s solve some examples and practice problems to understand the concept better.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-solved-examples-on-the-area-of-parallelogram\">Solved Examples on the Area of Parallelogram<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 1: A field has the shape of a parallelogram. The length of one side is 10 yards, and the corresponding height is 6 yards. Find the area of the field.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">One side of the parallelogram = 10 yards&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Corresponding height = 6 yards<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area of a parallelogram = A = base $\\times$ height.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = 10 yards $\\times$ 6 yards = 60 square yards.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the area of the field is 60 square yards.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 2: Calculate the area of a parallelogram whose diagonals are 15 units and 20 units, and the angle of intersection between the diagonals is 30\u00b0.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let d<sub>1 <\/sub>= 15 units and d<sub>2<\/sub>= 20 units.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using the formula for the area of a parallelogram with the lengths of its diagonals:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = $\\frac{1}{2} \\times d_{1} \\times d_{2} \\times sin(x)$\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = $\\frac{1}{2} \\times 15 \\times 20 \\times sin$(<strong>30\u00b0<\/strong>)\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = $\\frac{1}{2} \\times 15 \\times 20 \\times \\frac{1}{2}$1\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = $15 \\times 5$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = 75 square units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the area of the parallelogram is 75 square units.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 3: Find the area of a parallelogram when two parallel sides are 40 units and 20 units respectively and the angle between them is <\/strong><strong>6<\/strong><strong>0<\/strong><strong>.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Length of First Side = 40 units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Length of Second Side = 20 units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle between Both Sides = <strong>60\u00b0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using the Area of Parallelogram Formula,&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = a $\\times$ b $\\times$ sin(\u03b8)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area of Parallelogram = 40 $\\times$ 20 $\\times$ sin(<strong>60\u00b0<\/strong>)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area of Parallelogram = 800 $\\times$ sin(<strong>60\u00b0<\/strong>)\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area of Parallelogram = 800 $\\times$ 0.866<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area of Parallelogram = 692.8 square units.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the area of the parallelogram is 692.8 square units.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-practice-problems-on-the-area-of-parallelogram\">Practice Problems on the Area of Parallelogram<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Area of Parallelogram - Formula, Vector Form, Facts, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the formula for finding the area of a parallelogram?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Area = base $\\times$ height<\/div><div class=\"spq_answer_block\" data-value=\"1\">Area = length $\\times$ width<\/div><div class=\"spq_answer_block\" data-value=\"2\">Area = $\\frac{(base + height)}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">Area = $\\pi \\times$  radius\u00b2<\/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: Area = base $\\times$ height<br\/>Area = base $\\times$ height is the formula specifically used to calculate the area of a parallelogram.<\/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\">In a parallelogram, which sides are used to determine the base and height for calculating the area?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Adjacent sides<\/div><div class=\"spq_answer_block\" data-value=\"1\">Opposite sides<\/div><div class=\"spq_answer_block\" data-value=\"2\">Diagonal sides<\/div><div class=\"spq_answer_block\" data-value=\"3\">All sides have the same role<\/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: Opposite sides<br\/>The base of a parallelogram is one of the parallel sides, and the height is the perpendicular distance between the base and the opposite parallel side.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following CAN NOT be used to calculate the area of a parallelogram?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Base and height<\/div><div class=\"spq_answer_block\" data-value=\"1\">Length of adjacent sides and angle between them<\/div><div class=\"spq_answer_block\" data-value=\"2\">Perimeter of the parallelogram<\/div><div class=\"spq_answer_block\" data-value=\"3\">Diagonals and angle between them<\/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: Perimeter of the parallelogram<br\/>We cannot calculate the area of a parallelogram using its perimeter.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">If the base of a parallelogram is 8 units and the height is 10 units, what is the area?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">13 square units<\/div><div class=\"spq_answer_block\" data-value=\"1\">80 square units<\/div><div class=\"spq_answer_block\" data-value=\"2\">40 square units<\/div><div class=\"spq_answer_block\" data-value=\"3\">45 square units<\/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: 80 square units<br\/>Area = base $\\times$ height = 8 $\\times$ 10 = 80 square units<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Two parallelograms have the same height, but one has a base twice as long as the other. How does the area of the larger parallelogram compare to the smaller one?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">It is half the area of the smaller parallelogram.<\/div><div class=\"spq_answer_block\" data-value=\"1\">It is equal to the area of the smaller parallelogram.<\/div><div class=\"spq_answer_block\" data-value=\"2\">It is twice the area of the smaller parallelogram.<\/div><div class=\"spq_answer_block\" data-value=\"3\">It is four times the area of the smaller parallelogram.<\/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: It is twice the area of the smaller parallelogram.<br\/>Area of the smaller parallelogram = base $\\times$ height = bh<br>\r\nArea of the larger parallelogram = (2 $\\times$ base) $\\times$ height = 2bh = Twice the area of the smaller parallelogram<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Area of Parallelogram - Formula, Vector Form, Facts, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Area of Parallelogram\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the formula for finding the area of a parallelogram?\",\n                    \"text\": \"What is the formula for finding the area of a parallelogram?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Area = base $$\\\\times$$ height is the formula specifically used to calculate the area of a parallelogram.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Area = length $$\\\\times$$ width\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area = base $$\\\\times$$ height is the formula 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radius\u00b2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area = base $$\\\\times$$ height is the formula specifically used to calculate the area of a parallelogram.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Area = base $$\\\\times$$ height\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Area = base $$\\\\times$$ height is the formula specifically used to calculate the area of a parallelogram.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Area = base $$\\\\times$$ height is the formula specifically used to calculate the area of a parallelogram.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"In a parallelogram, which sides are used to determine the base and height for calculating the area?\",\n                    \"text\": \"In a parallelogram, which sides are used to determine the base and height for calculating the area?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The base of a parallelogram is one of the parallel sides, and the height is the perpendicular distance between the base and the opposite parallel side.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Adjacent sides\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The base of a parallelogram is one of the parallel sides, and the height is the perpendicular distance between the base and the opposite parallel side.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Diagonal sides\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The base of a parallelogram is one of the parallel sides, and the height is the perpendicular distance between the base and the opposite parallel side.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"All sides have the same role\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The base of a parallelogram is one of the parallel sides, and the height is the perpendicular distance between the base and the opposite parallel side.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Opposite sides\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The base of a parallelogram is one of the parallel sides, and the height is the perpendicular distance between the base and the opposite parallel side.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The base of a parallelogram is one of the parallel sides, and the height is the perpendicular distance between the base and the opposite parallel side.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following CAN NOT be used to calculate the area of a parallelogram?\",\n                    \"text\": \"Which of the following CAN NOT be used to calculate the area of a parallelogram?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We cannot calculate the area of a parallelogram using its perimeter.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Base and height\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We cannot calculate the area of a parallelogram using its perimeter.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Length of adjacent sides and angle between them\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We cannot calculate the area of a parallelogram using its perimeter.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Diagonals and angle between them\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We cannot calculate the area of a parallelogram using its perimeter.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Perimeter of the parallelogram\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We cannot calculate the area of a parallelogram using its perimeter.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We cannot calculate the area of a parallelogram using its perimeter.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the base of a parallelogram is 8 units and the height is 10 units, what is the area?\",\n                    \"text\": \"If the base of a parallelogram is 8 units and the height is 10 units, what is the area?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Area = base $$\\\\times$$ height = 8 $$\\\\times$$ 10 = 80 square units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"13 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area = base $$\\\\times$$ height = 8 $$\\\\times$$ 10 = 80 square units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"40 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area = base $$\\\\times$$ height = 8 $$\\\\times$$ 10 = 80 square units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"45 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area = base $$\\\\times$$ height = 8 $$\\\\times$$ 10 = 80 square units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"80 square units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Area = base $$\\\\times$$ height = 8 $$\\\\times$$ 10 = 80 square units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Area = base $$\\\\times$$ height = 8 $$\\\\times$$ 10 = 80 square units\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Two parallelograms have the same height, but one has a base twice as long as the other. How does the area of the larger parallelogram compare to the smaller one?\",\n                    \"text\": \"Two parallelograms have the same height, but one has a base twice as long as the other. How does the area of the larger parallelogram compare to the smaller one?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Area of the smaller parallelogram = base $$\\\\times$$ height = bh<br>\r\nArea of the larger parallelogram = (2 $$\\\\times$$ base) $$\\\\times$$ height = 2bh = Twice the area of the smaller parallelogram\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"It is half the area of the smaller parallelogram.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of the smaller parallelogram = base $$\\\\times$$ height = bh<br>\r\nArea of the larger parallelogram = (2 $$\\\\times$$ base) $$\\\\times$$ height = 2bh = Twice the area of the smaller parallelogram\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"It is equal to the area of the smaller parallelogram.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of the smaller parallelogram = base $$\\\\times$$ height = bh<br>\r\nArea of the larger parallelogram = (2 $$\\\\times$$ base) $$\\\\times$$ height = 2bh = Twice the area of the smaller parallelogram\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"It is four times the area of the smaller parallelogram.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of the smaller parallelogram = base $$\\\\times$$ height = bh<br>\r\nArea of the larger parallelogram = (2 $$\\\\times$$ base) $$\\\\times$$ height = 2bh = Twice the area of the smaller parallelogram\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"It is twice the area of the smaller parallelogram.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Area of the smaller parallelogram = base $$\\\\times$$ height = bh<br>\r\nArea of the larger parallelogram = (2 $$\\\\times$$ base) $$\\\\times$$ height = 2bh = Twice the area of the smaller parallelogram\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Area of the smaller parallelogram = base $$\\\\times$$ height = bh<br>\r\nArea of the larger parallelogram = (2 $$\\\\times$$ base) $$\\\\times$$ height = 2bh = Twice the area of the smaller parallelogram\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-frequently-asked-questions-on-the-area-of-parallelogram\">Frequently Asked Questions on the Area of Parallelogram<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-7c0cde02-c504-4f52-880b-8d042572a2f1\" 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-0-7c0cde02-c504-4f52-880b-8d042572a2f1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7c0cde02-c504-4f52-880b-8d042572a2f1\"><strong>Can any side of a parallelogram be considered as the base?<\/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-0-7c0cde02-c504-4f52-880b-8d042572a2f1\">\n\n<p class=\"wp-block-paragraph\">Yes, any of the parallel sides can be chosen as the base.<\/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-1-7c0cde02-c504-4f52-880b-8d042572a2f1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7c0cde02-c504-4f52-880b-8d042572a2f1\"><strong>How is the height of a parallelogram measured?<\/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-1-7c0cde02-c504-4f52-880b-8d042572a2f1\">\n\n<p class=\"wp-block-paragraph\">The height is the perpendicular distance between the base and the opposite parallel 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-2-7c0cde02-c504-4f52-880b-8d042572a2f1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7c0cde02-c504-4f52-880b-8d042572a2f1\"><strong>What happens to the area of a parallelogram if the base is doubled?<\/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-2-7c0cde02-c504-4f52-880b-8d042572a2f1\">\n\n<p class=\"wp-block-paragraph\">If the base of a parallelogram is doubled while the height remains the same, the area will also be doubled.<\/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-3-7c0cde02-c504-4f52-880b-8d042572a2f1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7c0cde02-c504-4f52-880b-8d042572a2f1\"><strong>How is the area of a parallelogram affected if the height is halved?<\/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-3-7c0cde02-c504-4f52-880b-8d042572a2f1\">\n\n<p class=\"wp-block-paragraph\">If the height of a parallelogram is halved while the base remains the same, the area will be halved.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Area of Parallelogram? The area of a parallelogram is defined as the measure of the two-dimensional space enclosed within its boundaries. It is calculated by multiplying the length of the base by its height, which is the perpendicular distance between the base and the opposite side. A parallelogram is a special quadrilateral &#8230; <a title=\"Area of Parallelogram &#8211; Formula, Vector Form, Facts, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-parallelogram\" aria-label=\"More on Area of Parallelogram &#8211; Formula, Vector Form, Facts, Examples, 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-33996","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\/33996","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=33996"}],"version-history":[{"count":8,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33996\/revisions"}],"predecessor-version":[{"id":34015,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33996\/revisions\/34015"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=33996"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=33996"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=33996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}