{"id":26493,"date":"2023-03-18T09:56:19","date_gmt":"2023-03-18T09:56:19","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26493"},"modified":"2024-02-05T15:40:24","modified_gmt":"2024-02-05T15:40:24","slug":"area-of-a-quarter-circle-definition-formula-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-quarter-circle","title":{"rendered":"Area of a Quarter Circle: Definition, Formula, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-6e1d7172-fce6-4c4b-9ca6-14bb76c1e898\" 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-a-quarter-circle#0-what-is-the-area-of-a-quarter-circle>What Is the Area of a Quarter Circle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-quarter-circle#2-area-of-quarter-circle-formula-using-radius>Area of Quarter Circle: Formula Using Radius<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-quarter-circle#4-how-to-find-the-area-of-a-quarter-circle>How To Find the Area of a Quarter Circle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-quarter-circle#7-solved-examples-on-area-of-a-quarter-circle>Solved Examples on Area of a Quarter Circle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-quarter-circle#8-practice-problems-on-area-of-a-quarter-circle>Practice Problems on Area of a Quarter Circle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-quarter-circle#9-frequently-asked-questions-on-area-of-a-quarter-circle>Frequently Asked Questions on Area of a Quarter Circle<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-area-of-a-quarter-circle\">What Is the Area of a Quarter Circle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>One-fourth of the area of a whole circle is called the area of a quarter of a circle. Area of a quarter circle is also known as the area of a quadrant.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The following image shows division of a circle in four quarters.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"352\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/division-of-circle-in-quarters.png\" alt=\"Division of circle in quarters\" class=\"wp-image-37765\" title=\"Division of circle in quarters\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/division-of-circle-in-quarters.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/division-of-circle-in-quarters-300x170.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Have you ever noticed how a pizza slice looks after we cut a whole pizza into four equal pieces? This one-fourth part of a circle is called a quarter circle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/comparing-a-pizza-slice-to-a-quarter-circle.png\" alt=\"Comparing a pizza slice to a quarter circle\" class=\"wp-image-37767\" title=\"Comparing a pizza slice to a quarter circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/comparing-a-pizza-slice-to-a-quarter-circle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/comparing-a-pizza-slice-to-a-quarter-circle-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">A quarter of anything means one-fourth of that object or thing. Thus, by a quarter of a circle, we mean one-fourth of the circle. Four of these shapes will make up a full circle. We can also get a quarter circle by dividing a semicircle into two halves.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-area-of-a-quarter-circle-definition\">Area of a Quarter Circle Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">In mathematical terms, the area created by two perpendicular radii and one-fourth area of the circumference of a whole circle is called the area of a quarter circle. It is also often referred to as a quadrant. These quadrants are all equal in size and area.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If we divide the area of a particular circle by 4, we can get the area of a quarter circle. It\u2019s that easy!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"292\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/formula-of-area-of-circle.png\" alt=\"Formula of area of circle\" class=\"wp-image-37768\" title=\"Formula of area of circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/formula-of-area-of-circle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/formula-of-area-of-circle-300x141.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Consider a circle with a radius \u201cr\u201d and a diameter \u201cd.\u201d&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that the area of a circle is calculated using the formula $\\pi r^2$ .<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here,$\\pi = 3.14 = \\frac{22}{7}$ .&nbsp;<\/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 href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-with-unit-squares-and-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_unit_sq_side_length_pt.png\" alt=\"Area with Unit Squares and Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area with Unit Squares and Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-word-problems-on-product-of-fractions\" 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\/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\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_grannys_rescue_3_4_5_gm.png\" alt=\"Build 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\">Build 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\/count-upto-10-objects-in-circle\" 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\/count_comp_hide_and_seek_10_gm.png\" alt=\"Count upto 10 Objects in Circle 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\">Count upto 10 Objects in Circle 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-area-of-rectilinear-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_rectilinear_shapes_pt.png\" alt=\"Determine the Area of Rectilinear 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\/express-quarter-hours-in-digital-format\" 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\/time_qrtr_hrs_tell_time_ac_pt.png\" alt=\"Express Quarter Hours in Digital Format 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\">Express Quarter Hours in Digital Format 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><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 eplus-wrapper\" id=\"2-area-of-quarter-circle-formula-using-radius\">Area of Quarter Circle: Formula Using Radius<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The radius of a quarter of a circle is the same as the radius of the given circle.So let\u2019s say if a circle has a length of radius \u201cr,\u201d then the area of circle $= \\pi r^2$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">A quarter circle is $\\frac{1}{4}$ of the area of a whole circle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"374\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/area-of-a-quarter-circle-visual.png\" alt=\"Area of a quarter circle visual\" class=\"wp-image-37769\" title=\"Area of a quarter circle visual\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/area-of-a-quarter-circle-visual.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/area-of-a-quarter-circle-visual-300x181.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Now, by dividing the area of the whole circle by 4, we can get the formula for a quarter circle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the area of a quarter circle $= \\frac{\\pi r^2}{4}$ or $\\frac{1}{4} \\pi r^2$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"197\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/area-of-quarter-circle.png\" alt=\"Area of quarter circle\" class=\"wp-image-37770\" title=\"Area of quarter circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/area-of-quarter-circle.png 344w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/area-of-quarter-circle-300x172.png 300w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/figure>\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\" 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-mixed-numbers-and-fractions-using-area-models.jpeg\" alt=\"Add Mixed Numbers and 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\/circle-equivalent-fractions\" 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\/circle-equivalent-fractions.jpeg\" alt=\"Circle Equivalent Fractions 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\/compare-fractions-using-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\/compare-fractions-using-area-model.jpeg\" alt=\"Compare Fractions Using 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-area-of-a-quarter-circle-formula-using-diameter\">Area of a Quarter Circle: Formula Using Diameter<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">For any circle, its diameter is double of its radius.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, $d = 2r$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We may calculate the area of a quarter circle in terms of diameter by substituting this value into the formula above.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Then, the area of circle $= (\\frac{d}{2})^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;      $= \\frac{\\pi d^2}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of a quarter circle $= \\frac{1}{4} \\times \\frac{\\pi d^2}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{\\pi d^2}{16}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;Thus, the area of a quarter circle in terms of diameter $= \\frac{\\pi d^2}{16}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-how-to-find-the-area-of-a-quarter-circle\">How To Find the Area of a Quarter Circle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1:<\/strong> Note down the given radius or the diameter of the circle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2:<\/strong> If the radius \u201cr\u201d is given, substitute the value of \u201cr\u201d in the formula $\\frac{\\pi r^2}{4}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3: <\/strong>If the diameter \u201cd\u201d is given, substitute the value of \u201cd\u201d in the formula $\\frac{\\pi d^2}{16}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4: <\/strong>Area is measured in square units. Don\u2019t forget to assign the appropriate unit to the calculated value of the area of a quarter circle.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-facts-about-area-of-a-quarter-circle\">Facts about Area of a Quarter Circle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">1. A circle is a two-dimensional shape and so is the quarter circle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">2. A quarter circle is formed when a circle is divided into four equal portions.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">3. A quarter circle can also be formed by dividing a semicircle into two equal parts.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">4. A quarter circle is also known as a quadrant.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">5. The circumference of a quarter circle is one-fourth of that of a circle with the same radius.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The area of a quarter circle is one fourth of the area of a circle. In this article, we learned in detail about the area of the quarter circle, formulas. Let\u2019s solve a few examples and practice problems for better understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-solved-examples-on-area-of-a-quarter-circle\">Solved Examples on Area of a Quarter Circle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1.<\/strong> <strong>Linda ordered a 12-inch pizza for herself and her 3 friends. They want to share the pizza equally among themselves. Find the quantity of pizza each one got. (Use <\/strong>$ \\pi = 3.14<strong>)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given data: The diameter of the pizza $= 12$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$ \\pi = 3.14$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that the area of a quarter circle in terms of diameter $= \\frac{\\pi d^2}{16}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;So,&nbsp; $A = \\frac{3.14 \\times (12)^2}{16}$ &nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong>$= \\frac{3.14 \\times 144}{16}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/strong>$= \\frac{452.16}{16}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 28.26$ square inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The quantity of pizza each one got is 28.26 $in^2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Find the area of the quarter circle with the help of the image given below.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"213\" height=\"213\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-circle-with-radius-7-in.png\" alt=\"A circle with radius 7 in\" class=\"wp-image-37771\" title=\"A circle with radius 7 in\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-circle-with-radius-7-in.png 213w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-circle-with-radius-7-in-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-circle-with-radius-7-in-120x120.png 120w\" sizes=\"auto, (max-width: 213px) 100vw, 213px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given data:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The radius of the circle $= 7$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that the area of a quarter circle in terms of its radius $= \\frac{\\pi r^2}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$A =\\frac{\\pi r^2}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{3.14 \\times 7^2}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{3.14 \\times 49}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{153.86}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$A&nbsp; = 38.46$ square inches<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of the quarter circle $= 38.46\\; in^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. The radius of a quarter circle shaped table is 3 ft. What is the area of the table? ( Use <\/strong>$ \\pi = 3.14$<strong>)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given data:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The radius of the table $= 3$ ft<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that the area of a quarter circle in terms of its radius $=&nbsp;\\frac{\\pi r^2}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$A = \\frac{\\pi r^2}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{3.14 \\times 3^2}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{3.14 \\times 9}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{28.26}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=&nbsp; 7.065$ square ft.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of the quarter circle shaped table $= 7.065\\; ft^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. A circular park has a diameter of 50 yards. Only a quarter of the park is allotted for an open gym. Find the area allotted for the gym.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given data: Diameter of the park $= 50$ yards<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that the area of a quarter circle in terms of diameter $= \\frac{\\pi d^2}{16}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;So,&nbsp; $A = \\frac{3.14 \\times(50)^2}{16}$  &nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{3.14 \\times 2500}{16}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $= \\frac{7850}{16}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 490.62$ square yards<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of the park allotted for the gym is 490.62 square yards.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-practice-problems-on-area-of-a-quarter-circle\">Practice Problems on Area of a Quarter Circle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Area of a Quarter Circle: Definition, Formula, Examples<\/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\">Which of the following is NOT a formula for finding the area of a quarter circle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\"> $\\frac{1}{4}\\pi r2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{\\pi d^2}{16}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{\\pi r^2}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{\\pi r^2}{4}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{\\pi r^2}{2}$<br\/> $\\frac{1}{4}\\pi r2$  and $\\frac{\\pi r2}{4}$  are the formulas for finding the area of a quarter circle in terms of its radius. $\\frac{\\pi d^2}{16}$  is the formula for finding the area of a quarter circle in terms of its diameter. $\\frac{\\pi r^2}{2}$ is the formula of the area of the semicircle.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What fraction of a circle is a quadrant ?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{3}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/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: $\\frac{1}{4}$<br\/>A quadrant of a circle is each quarter of a circle. When four quadrants are joined together, it forms a circle.<\/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\">If the area of a circle is 4 square units, the area of a quarter circle is ________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">8<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">1<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/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: 1<br\/>Area of a quarter circle is $\\frac{1}{4}$  of the total area of a circle. So, if we divide the area of the given circle by 4, we can get the area of a quarter circle. Thus, area of quarter circle $= \\frac{4}{4} = 1$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which of the following statements is not correct?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">quarter circle is formed when a circle is divided into four equal portions.<\/div><div class=\"spq_answer_block\" data-value=\"1\">Quadrants are all equal in size and area.<\/div><div class=\"spq_answer_block\" data-value=\"2\">A quarter circle is a three-dimensional shape.<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/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: A quarter circle is a three-dimensional shape.<br\/>A circle is a two-dimensional shape and so is the quarter circle.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Which of the following is the unit of measuring area of a quarter circle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">unit<\/div><div class=\"spq_answer_block\" data-value=\"1\">unit square<\/div><div class=\"spq_answer_block\" data-value=\"2\">unit cube<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/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: unit square<br\/>The unit of area is the square unit, for example, square yards, \\[\\text{in}^{2}, \\text{ft}^{2},\\] etc.<\/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 a Quarter Circle: Definition, Formula, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Area of a Quarter Circle\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is NOT a formula for finding the area of a quarter circle?\",\n                    \"text\": \"Which of the following is NOT a formula for finding the area of a quarter circle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \" $$\\\\frac{1}{4}\\\\pi r2$$  and $$\\\\frac{\\\\pi r2}{4}$$  are the formulas for finding the area of a quarter circle in terms of its radius. $$\\\\frac{\\\\pi d^2}{16}$$  is the formula for finding the area of a quarter circle in terms of its diameter. $$\\\\frac{\\\\pi r^2}{2}$$ is the formula of the area of the semicircle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \" $$\\\\frac{1}{4}\\\\pi r2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \" $$\\\\frac{1}{4}\\\\pi r2$$  and $$\\\\frac{\\\\pi r2}{4}$$  are the formulas for finding the area of a quarter circle in terms of its radius. $$\\\\frac{\\\\pi d^2}{16}$$  is the formula for finding the area of a quarter circle in terms of its diameter. $$\\\\frac{\\\\pi r^2}{2}$$ is the formula of the area of the semicircle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{\\\\pi d^2}{16}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \" $$\\\\frac{1}{4}\\\\pi r2$$  and $$\\\\frac{\\\\pi r2}{4}$$  are the formulas for finding the area of a quarter circle in terms of its radius. $$\\\\frac{\\\\pi d^2}{16}$$  is the formula for finding the area of a quarter circle in terms of its diameter. $$\\\\frac{\\\\pi r^2}{2}$$ is the formula of the area of the semicircle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{\\\\pi r^2}{4}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \" $$\\\\frac{1}{4}\\\\pi r2$$  and $$\\\\frac{\\\\pi r2}{4}$$  are the formulas for finding the area of a quarter circle in terms of its radius. $$\\\\frac{\\\\pi d^2}{16}$$  is the formula for finding the area of a quarter circle in terms of its diameter. $$\\\\frac{\\\\pi r^2}{2}$$ is the formula of the area of the semicircle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{\\\\pi r^2}{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \" $$\\\\frac{1}{4}\\\\pi r2$$  and $$\\\\frac{\\\\pi r2}{4}$$  are the formulas for finding the area of a quarter circle in terms of its radius. $$\\\\frac{\\\\pi d^2}{16}$$  is the formula for finding the area of a quarter circle in terms of its diameter. $$\\\\frac{\\\\pi r^2}{2}$$ is the formula of the area of the semicircle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \" $$\\\\frac{1}{4}\\\\pi r2$$  and $$\\\\frac{\\\\pi r2}{4}$$  are the formulas for finding the area of a quarter circle in terms of its radius. $$\\\\frac{\\\\pi d^2}{16}$$  is the formula for finding the area of a quarter circle in terms of its diameter. $$\\\\frac{\\\\pi r^2}{2}$$ is the formula of the area of the semicircle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What fraction of a circle is a quadrant ?\",\n                    \"text\": \"What fraction of a circle is a quadrant ?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A quadrant of a circle is each quarter of a circle. When four quadrants are joined together, it forms a circle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{3}{4}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A quadrant of a circle is each quarter of a circle. When four quadrants are joined together, it forms a circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A quadrant of a circle is each quarter of a circle. When four quadrants are joined together, it forms a circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A quadrant of a circle is each quarter of a circle. When four quadrants are joined together, it forms a circle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{4}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A quadrant of a circle is each quarter of a circle. When four quadrants are joined together, it forms a circle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A quadrant of a circle is each quarter of a circle. When four quadrants are joined together, it forms a circle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the area of a circle is 4 square units, the area of a quarter circle is ________.\",\n                    \"text\": \"If the area of a circle is 4 square units, the area of a quarter circle is ________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Area of a quarter circle is $$\\\\frac{1}{4}$$  of the total area of a circle. So, if we divide the area of the given circle by 4, we can get the area of a quarter circle. Thus, area of quarter circle $$= \\\\frac{4}{4} = 1$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of a quarter circle is $$\\\\frac{1}{4}$$  of the total area of a circle. So, if we divide the area of the given circle by 4, we can get the area of a quarter circle. Thus, area of quarter circle $$= \\\\frac{4}{4} = 1$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of a quarter circle is $$\\\\frac{1}{4}$$  of the total area of a circle. So, if we divide the area of the given circle by 4, we can get the area of a quarter circle. Thus, area of quarter circle $$= \\\\frac{4}{4} = 1$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of a quarter circle is $$\\\\frac{1}{4}$$  of the total area of a circle. So, if we divide the area of the given circle by 4, we can get the area of a quarter circle. Thus, area of quarter circle $$= \\\\frac{4}{4} = 1$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Area of a quarter circle is $$\\\\frac{1}{4}$$  of the total area of a circle. So, if we divide the area of the given circle by 4, we can get the area of a quarter circle. Thus, area of quarter circle $$= \\\\frac{4}{4} = 1$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Area of a quarter circle is $$\\\\frac{1}{4}$$  of the total area of a circle. So, if we divide the area of the given circle by 4, we can get the area of a quarter circle. Thus, area of quarter circle $$= \\\\frac{4}{4} = 1$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following statements is not correct?\",\n                    \"text\": \"Which of the following statements is not correct?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A circle is a two-dimensional shape and so is the quarter circle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"quarter circle is formed when a circle is divided into four equal portions.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A circle is a two-dimensional shape and so is the quarter circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Quadrants are all equal in size and area.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A circle is a two-dimensional shape and so is the quarter circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A circle is a two-dimensional shape and so is the quarter circle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"A quarter circle is a three-dimensional shape.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A circle is a two-dimensional shape and so is the quarter circle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A circle is a two-dimensional shape and so is the quarter circle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is the unit of measuring area of a quarter circle?\",\n                    \"text\": \"Which of the following is the unit of measuring area of a quarter circle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The unit of area is the square unit, for example, square yards, \\\\[\\\\text{in}^{2}, \\\\text{ft}^{2},\\\\] etc.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"unit\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The unit of area is the square unit, for example, square yards, \\\\[\\\\text{in}^{2}, \\\\text{ft}^{2},\\\\] etc.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"unit cube\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The unit of area is the square unit, for example, square yards, \\\\[\\\\text{in}^{2}, \\\\text{ft}^{2},\\\\] etc.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The unit of area is the square unit, for example, square yards, \\\\[\\\\text{in}^{2}, \\\\text{ft}^{2},\\\\] etc.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"unit square\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The unit of area is the square unit, for example, square yards, \\\\[\\\\text{in}^{2}, \\\\text{ft}^{2},\\\\] etc.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The unit of area is the square unit, for example, square yards, \\\\[\\\\text{in}^{2}, \\\\text{ft}^{2},\\\\] etc.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-frequently-asked-questions-on-area-of-a-quarter-circle\">Frequently Asked Questions on Area of a Quarter Circle<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-7a891acc-cc82-43b7-bcbf-c0342b052445\" 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-0-7a891acc-cc82-43b7-bcbf-c0342b052445\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7a891acc-cc82-43b7-bcbf-c0342b052445\"><strong>How to find the area of the part outside of the quarter circle?<\/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-0-7a891acc-cc82-43b7-bcbf-c0342b052445\">\n\n<p class=\"eplus-wrapper\">Quarter circle is the $\\frac{1}{4}$th part&nbsp; of the circle. While outside of the quarter circle is $\\frac{3}{4}$th part of the circle. We know that area of quarter circle $= \\farc{\\pi r^2}{4}$ and the area of the circle $= \\pi r^2$. Simply subtract the area of the quarter circle from the area of the whole circle. The final result will be the surface area of the part outside of the quarter circle or the $\\frac{3}{4}$th part.<\/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-1-7a891acc-cc82-43b7-bcbf-c0342b052445\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7a891acc-cc82-43b7-bcbf-c0342b052445\"><strong>Are the circumference and perimeter of the quarter circle the same?<\/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-1-7a891acc-cc82-43b7-bcbf-c0342b052445\">\n\n<p class=\"eplus-wrapper\">Yes, circumference is the length of the boundary of the circle. It follows the same principle behind finding the perimeter of any curved geometrical 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-2-7a891acc-cc82-43b7-bcbf-c0342b052445\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7a891acc-cc82-43b7-bcbf-c0342b052445\"><strong>How can we find the area of a quarter circle in a 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-2-7a891acc-cc82-43b7-bcbf-c0342b052445\">\n\n<p class=\"eplus-wrapper\">Take a look at the image given below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"272\" height=\"268\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/quarter-circle-in-a-square.png\" alt=\"Quarter circle in a square\" class=\"wp-image-37772\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Let the side of the square be s.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Side of the square $=$ Radius of the circle $= \\;s\\; =$ Radius of the quarter circleArea of a quarter circle $=\\frac{\\pi r^2} {4} = \\frac{\\pi s^2}{4}$<\/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-3-7a891acc-cc82-43b7-bcbf-c0342b052445\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7a891acc-cc82-43b7-bcbf-c0342b052445\"><strong>What is the perimeter of the quadrant of the circle?<\/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-3-7a891acc-cc82-43b7-bcbf-c0342b052445\">\n\n<p class=\"eplus-wrapper\">The perimeter of a quadrant of the circle is one-fourth of the circumference of the circle and twice the radius of the circle.Perimeter $(P)$ of a quadrant of a circle $= \\frac{2 \\pi r}{4} + 2r$<\/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-4-7a891acc-cc82-43b7-bcbf-c0342b052445\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7a891acc-cc82-43b7-bcbf-c0342b052445\"><strong>What is the formula to find the arc length of the quarter circle?<\/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-4-7a891acc-cc82-43b7-bcbf-c0342b052445\">\n\n<p class=\"eplus-wrapper\">The arc length of a quarter circle with radius \u201cr\u201d and diameter \u201cd\u201d&nbsp; is nothing but $\\frac{1}{4}$th the circumference of the circle. It is given by $\\frac{2 \\pi r}{4}$ or $\\frac{\\pi r}{2}$.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Area of a Quarter Circle? One-fourth of the area of a whole circle is called the area of a quarter of a circle. Area of a quarter circle is also known as the area of a quadrant.&nbsp; The following image shows division of a circle in four quarters. Have you ever noticed &#8230; <a title=\"Area of a Quarter Circle: Definition, Formula, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-quarter-circle\" aria-label=\"More on Area of a Quarter Circle: Definition, Formula, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-26493","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\/26493","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=26493"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26493\/revisions"}],"predecessor-version":[{"id":39947,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26493\/revisions\/39947"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26493"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26493"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26493"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}