{"id":23501,"date":"2023-02-03T08:31:43","date_gmt":"2023-02-03T08:31:43","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=23501"},"modified":"2024-02-05T09:10:31","modified_gmt":"2024-02-05T09:10:31","slug":"area-of-a-semicircle","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-semi-circle","title":{"rendered":"Area of a Semicircle"},"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-4b960f4b-4410-4eec-8725-8c69e7b5c287\" 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-semi-circle#0-semicircle-introduction>Semicircle: Introduction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-semi-circle#1-what-is-a-semicircle>What Is a Semicircle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-semi-circle#6-derivation>Derivation<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-semi-circle#10-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-semi-circle#11-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-semi-circle#12-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-semicircle-introduction\">Semicircle: Introduction<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In geometry, a semicircle is defined as a half circle formed by cutting the circle into two halves. Every diameter of a circle divides it into two semicircles.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We get a semicircle when we fold a circular piece along its diameter. So, a circle, when divided in two equal halves, gives us a semicircle.&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\/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><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-what-is-a-semicircle\">What Is a Semicircle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A semicircle is half of a circle. It is a plane figure formed when we divide a circle into two identical halves.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Take any two points on the circle such that the line joining these two points passes through the center of the circle. The two halves that we get are called semicircles. These two semicircles, when taken together, give us a complete circle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In the following image, O is the center. The diameter BC divides the circle into two semicircles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"517\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/semicircles.webp\" alt=\"Semicircles\" class=\"wp-image-32585\" title=\"Semicircles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/semicircles.webp 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/semicircles-300x250.webp 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/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 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 href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-the-equation-for-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-equation-for-the-area-model.jpeg\" alt=\"Complete the Equation for 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 href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/convert-mixed-numbers-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\/convert-mixed-numbers-using-area-models.jpeg\" alt=\"Convert Mixed Numbers 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\/create-area-models-to-multiply-unit-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\/create-area-models-to-multiply-unit-fractions.jpeg\" alt=\"Create Area Models to Multiply Unit 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\/create-equivalent-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\/create-equivalent-fractions-using-area-model.jpeg\" alt=\"Create Equivalent 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><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-semicircle-shape\">Semicircle Shape<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">To obtain a semicircular shape, we can simply cut the circle from the center.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So we could also say that the area of the semicircle is just half of that of the circle.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">This can be easily understood with the help of the figure given below.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"453\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/semicircle-shape-formed-by-the-diameter.webp\" alt=\"Semicircle shape formed by the diameter\" class=\"wp-image-32587\" title=\"Semicircle shape formed by the diameter\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/semicircle-shape-formed-by-the-diameter.webp 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/semicircle-shape-formed-by-the-diameter-300x219.webp 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Consider the diameter AB of the given circle. This diameter AB divides the given circle into two identical halves. These halves are semicircles and the area of these two semicircles, when combined, gives the area of the entire circle.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-area-of-semicircle\">Area of Semicircle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We know that the area of a circle is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Area of circle <\/strong>$= \\pi r^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">where,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\pi&nbsp; = 3.1415$ or $\\frac{22}{7}$ , and r is the radius of the circle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of the semicircle is half of the area of a circle. This gives us the desired formula, that is,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Area of semicircle <\/strong>$= \\frac{\\pi r^{2}}{2} = \\frac{1}{2} \\pi r^{2}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-how-to-find-the-area-of-a-semicircle\">How to Find the Area of a Semicircle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1:<\/strong> Note the radius of the circle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If the diameter is given, find the radius by dividing the diameter by 2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, the diameter of the circle is 14 inches, then the radius of the circle is 7 inches.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2:<\/strong> Find the area of the circle using the formula and by substituting the values of r and&nbsp; $\\pi$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{A} = \\pi r^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">You can use the value of \u03c0 as either 3.14 or $\\frac{22}{7}$, when not specified in the question.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In our example, $r = 7$ inches and use $\\pi = \\frac{22}{7}$&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, area of circle $= \\pi r^{2}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">area of circle $= \\frac{22}{7} \\times (7)^{2}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">area of circle $= 22 \\times 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">area of circle $= 154$ square inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3: <\/strong>Divide the area of the circle by 2 to obtain the area of the semicircle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of semicircle $= \\frac{\\pi r^{2}}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In the above example, Area of semicircle $= \\frac{154}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of semicircle $= 77\\; \\text{inches}^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of a semicircle is measured in \u201csquare units.\u201d<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-area-of-a-semicircle-using-diameter\">Area of a Semicircle Using Diameter<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We know that<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of semicircle $= \\frac{\\pi r^{2}}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $r = \\frac{d}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of semicircle $=\\frac{\\pi}{2} \\left[\\frac{d}{2}\\right]^{2}= \\frac{\u03c0d^{2}}{8}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-derivation\">Derivation<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We know that the area of any shape can also be determined with the help of the number of squares in that particular shape. So, we can say that the area of the circle can be measured by the number of square units fitting in that circle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Consider a circle shown below, containing isosceles triangles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"493\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/area-of-semicircle.webp\" alt=\"Area of semicircle\" class=\"wp-image-32589\" title=\"Area of semicircle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/area-of-semicircle.webp 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/area-of-semicircle-300x239.webp 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">All the radii of the circle are equal in length.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the polygon in the above figure can be easily divided into various (n) isosceles triangles (radius being two equal sides).&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">One such isosceles triangle can be represented as given below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"459\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/an-isosceles-triangle-formed-in-a-circle.webp\" alt=\"An isosceles triangle formed in a circle\" class=\"wp-image-32590\" title=\"An isosceles triangle formed in a circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/an-isosceles-triangle-formed-in-a-circle.webp 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/an-isosceles-triangle-formed-in-a-circle-300x222.webp 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Area of a triangle can be given as half times the product of its height and base.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In this given isosceles triangle, base $= s$ and height $= h$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of this isosceles triangle $= \\frac{1}{2} (h \\times s)$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Similarly, for n such isosceles triangles the area would be n times the area of one such triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of n such isosceles triangles $= \\frac{1}{2} (n \\times h \\times s)$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, the term $n \\times s$ gives the perimeter of the polygon. As the polygon happens to look more and more like a circle, the perimeter term approaches the circumference of the circle, which is given as $2\\pi r$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">When we substitute $2 \\times \\pi \\times r$ in place of $n \\times s$ we get,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of polygon $= &nbsp;12 (2\\pi r)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Also, as s approaches zero, which happens as the number of sides increase making the triangle narrower, h approaches to r (the value of h becomes very close to r). So we substitute, r in place of h to get:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of polygon $= \\frac{r}{2} (2 \\times \\pi \\times r)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of polygon $= \\frac{r}{2} (2 \\times \\pi \\times r)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of polygon $= \\frac{1}{2} (r \\times 2 \\times \\pi \\times r)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Rearrange it to get,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of circle $= \\pi r^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that the area of a semicircle equation is equal to half the area of the complete circle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of a semicircle $= \\frac{\\pi r^{2}}{2}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-area-of-semicircle-formula\">Area of Semicircle Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">So we derive the formula for the area of a semicircle as $(\\pi r^{2})\/2$, which is half the area of a circle.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Also, the surface area of the semicircle formula is the same as the area of the semicircle formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of semicircle $=\\frac{\\pi r^{2}}{2}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-fun-facts\">Fun Facts!<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Semicircle is obtained by cutting the circle into two exactly equal halves.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Area of a semicircle is half the area of a circle with the same radius.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Area of a semicircle with radius r can be given as $(\\pi r^{2})\/2$.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned about semicircles. We derived the formula for calculating the area of a given semicircle with the help of the area of a circle with a given radius. We also learned a few amazing facts related to semicircles. The concept was complemented by a few solved and a few unsolved questions related to the topic.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. If the radius of a semicircle is 49 inches, find its area.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>Area of semicircle $= \\frac{\\pi r^{2}}{2}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of semicircle $= \\frac{22}{7} \\times \\frac{49^{2}}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of semicircle $= 11 \\times 7 \\times 49$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of semicircle $= 3773\\; \\text{inches}^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. If the diameter of a semicircle is 70 inches, find its area of the semicircle with diameter.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> Area of Semicircle $= \\frac{\\pi r^{2}}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Radius $= \\frac{70}{2} = 35$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, Area of semicircle $= \\frac{22}{7} \\times \\frac{35^{2}}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of circle $= 11 \\times 5 \\times 35$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of circle $= 1925\\; \\text{inches}^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Find the area of the figure in which ABCD is a square of side 42 inches and CPD is a semicircle. <\/strong>$(\\text{Use}\\; \\pi = \\frac{22}{7})$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"324\" height=\"420\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/geometric-shape-composed-of-a-semicircle-and-a-square.webp\" alt=\"Geometric shape composed of a semicircle and a square\" class=\"wp-image-32592\" title=\"Geometric shape composed of a semicircle and a square\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/geometric-shape-composed-of-a-semicircle-and-a-square.webp 324w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/geometric-shape-composed-of-a-semicircle-and-a-square-231x300.webp 231w\" sizes=\"auto, (max-width: 324px) 100vw, 324px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The required area $=$ Area of the square $\\text{ABCD} +$ Area of the semicircle $\\text{CPD}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= a^{2} + \\frac{1}{2} \\pi r^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 42^{2} +&nbsp; \\frac{1}{2} \\times \\pi \\times (\\frac{1}{2} \\times 42)^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= (42^{2} +\\frac{1}{2} \\times \\frac{22}{7} \\times 21^{2})$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 1764 + 693$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 2457$ square inches<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. If the area of a circle is 100 square yards, what is the area of a semicircle?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of circle $=&nbsp; 100$ square yards<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of semicircle $= \\frac{100}{2}$ square yards<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. Hazel has a circular garden outside her house with a diameter of 12 yards. Hazel wants to mow exactly half of the garden. Find the area of the part she wants to mow.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Diameter $= 12$ yards<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area $= ?$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of a semicircle $= \\frac{\\pi r^{2}}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Radius $= \\frac{12}{2} = 6$ yards<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\pi = 3.142$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, area $= \\frac{3.142 \\times 6 \\times 6}{2} = 56.55$ square yards<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Area of a Semicircle<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The area of a semicircle is ____ the area of the circle.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Twice<\/div><div class=\"spq_answer_block\" data-value=\"1\">Half<\/div><div class=\"spq_answer_block\" data-value=\"2\">Thrice<\/div><div class=\"spq_answer_block\" data-value=\"3\">Equal to<\/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: Half<br\/>Radius of the semicircle is the same as the radius of the circle.<\/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\">A circle has a diameter of 14 inches. What is the area of the semicircle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">7 inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">77 square inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">343 square inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">49 square inches<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 77 square inches<br\/>$d = 14$ inches. So, $r = \\frac{14}{2} = 7$ inches<br>\r\nArea of semicircle $= \\frac{\\pi r^{2}}{2}$<br>\r\nArea of semicircle $= \\frac{22}{7} \\times \\frac{7^{2}}{2}$<br>\r\nArea of semicircle $= 77\\; \\text{inches}^{2}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The ____ of circle divides into two semicircles.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Radius<\/div><div class=\"spq_answer_block\" data-value=\"1\">Chord<\/div><div class=\"spq_answer_block\" data-value=\"2\">Tangent<\/div><div class=\"spq_answer_block\" data-value=\"3\">Diameter<\/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: Diameter<br\/>The diameter of a circle divides it into two equal parts, which are called semicircles.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Area of the semicircle shown below is ____.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Solved-Examples-2-1.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{9\\pi}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{3\\pi}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{\\pi}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{12\\pi}{2}$<\/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: $\\frac{9\\pi}{2}$<br\/>Area of complete circle $= \\pi r^2 = 9\\pi$<br>\r\nArea of semicircle $= \\frac{\\pi r^2}{2} =  \\frac{9\\pi}{2}$<\/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 Semicircle\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Area of a Semicircle\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The area of a semicircle is ____ the area of the circle.\",\n                    \"text\": \"The area of a semicircle is ____ the area of the circle.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Radius of the semicircle is the same as the radius of the circle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Twice\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Radius of the semicircle is the same as the radius of the circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Thrice\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Radius of the semicircle is the same as the radius of the circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Equal to\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Radius of the semicircle is the same as the radius of the circle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Half\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Radius of the semicircle is the same as the radius of the circle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Radius of the semicircle is the same as the radius of the circle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A circle has a diameter of 14 inches. What is the area of the semicircle?\",\n                    \"text\": \"A circle has a diameter of 14 inches. What is the area of the semicircle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$d = 14$$ inches. So, $$r = \\\\frac{14}{2} = 7$$ inches<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^{2}}{2}$$<br>\r\nArea of semicircle $$= \\\\frac{22}{7} \\\\times \\\\frac{7^{2}}{2}$$<br>\r\nArea of semicircle $$= 77\\\\; \\\\text{inches}^{2}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"7 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$d = 14$$ inches. So, $$r = \\\\frac{14}{2} = 7$$ inches<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^{2}}{2}$$<br>\r\nArea of semicircle $$= \\\\frac{22}{7} \\\\times \\\\frac{7^{2}}{2}$$<br>\r\nArea of semicircle $$= 77\\\\; \\\\text{inches}^{2}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"343 square inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$d = 14$$ inches. So, $$r = \\\\frac{14}{2} = 7$$ inches<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^{2}}{2}$$<br>\r\nArea of semicircle $$= \\\\frac{22}{7} \\\\times \\\\frac{7^{2}}{2}$$<br>\r\nArea of semicircle $$= 77\\\\; \\\\text{inches}^{2}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"49 square inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$d = 14$$ inches. So, $$r = \\\\frac{14}{2} = 7$$ inches<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^{2}}{2}$$<br>\r\nArea of semicircle $$= \\\\frac{22}{7} \\\\times \\\\frac{7^{2}}{2}$$<br>\r\nArea of semicircle $$= 77\\\\; \\\\text{inches}^{2}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"77 square inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$d = 14$$ inches. So, $$r = \\\\frac{14}{2} = 7$$ inches<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^{2}}{2}$$<br>\r\nArea of semicircle $$= \\\\frac{22}{7} \\\\times \\\\frac{7^{2}}{2}$$<br>\r\nArea of semicircle $$= 77\\\\; \\\\text{inches}^{2}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$d = 14$$ inches. So, $$r = \\\\frac{14}{2} = 7$$ inches<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^{2}}{2}$$<br>\r\nArea of semicircle $$= \\\\frac{22}{7} \\\\times \\\\frac{7^{2}}{2}$$<br>\r\nArea of semicircle $$= 77\\\\; \\\\text{inches}^{2}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The ____ of circle divides into two semicircles.\",\n                    \"text\": \"The ____ of circle divides into two semicircles.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The diameter of a circle divides it into two equal parts, which are called semicircles.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Radius\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diameter of a circle divides it into two equal parts, which are called semicircles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Chord\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diameter of a circle divides it into two equal parts, which are called semicircles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Tangent\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The diameter of a circle divides it into two equal parts, which are called semicircles.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Diameter\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The diameter of a circle divides it into two equal parts, which are called semicircles.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The diameter of a circle divides it into two equal parts, which are called semicircles.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Area of the semicircle shown below is ____.\",\n                    \"text\": \"Area of the semicircle shown below is ____. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Solved-Examples-2-1.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Area of complete circle $$= \\\\pi r^2 = 9\\\\pi$$<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^2}{2} =  \\\\frac{9\\\\pi}{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{3\\\\pi}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of complete circle $$= \\\\pi r^2 = 9\\\\pi$$<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^2}{2} =  \\\\frac{9\\\\pi}{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{\\\\pi}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of complete circle $$= \\\\pi r^2 = 9\\\\pi$$<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^2}{2} =  \\\\frac{9\\\\pi}{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{12\\\\pi}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Area of complete circle $$= \\\\pi r^2 = 9\\\\pi$$<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^2}{2} =  \\\\frac{9\\\\pi}{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{9\\\\pi}{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Area of complete circle $$= \\\\pi r^2 = 9\\\\pi$$<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^2}{2} =  \\\\frac{9\\\\pi}{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Area of complete circle $$= \\\\pi r^2 = 9\\\\pi$$<br>\r\nArea of semicircle $$= \\\\frac{\\\\pi r^2}{2} =  \\\\frac{9\\\\pi}{2}$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-6695220d-f47b-4362-a1ea-c52714d081e1\" 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-0-6695220d-f47b-4362-a1ea-c52714d081e1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6695220d-f47b-4362-a1ea-c52714d081e1\"><strong>What is a 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-0-6695220d-f47b-4362-a1ea-c52714d081e1\">\n\n<p class=\"eplus-wrapper\">If a circle is divided into four equal parts, then each part is called a \u201cquarter circle.\u201d Four quarter circles make a complete circle.<\/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-1-6695220d-f47b-4362-a1ea-c52714d081e1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6695220d-f47b-4362-a1ea-c52714d081e1\"><strong>What is circumference?<\/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-1-6695220d-f47b-4362-a1ea-c52714d081e1\">\n\n<p class=\"eplus-wrapper\">Circumference is the length of the boundary of the circle.<\/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-2-6695220d-f47b-4362-a1ea-c52714d081e1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6695220d-f47b-4362-a1ea-c52714d081e1\"><strong>What is the perimeter or circumference of the semicircle?<\/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-2-6695220d-f47b-4362-a1ea-c52714d081e1\">\n\n<p class=\"eplus-wrapper\">Perimeter of the semicircle $= \\pi r + d$, where d is the diameter of the circle.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Semicircle: Introduction In geometry, a semicircle is defined as a half circle formed by cutting the circle into two halves. Every diameter of a circle divides it into two semicircles.&nbsp; We get a semicircle when we fold a circular piece along its diameter. So, a circle, when divided in two equal halves, gives us a &#8230; <a title=\"Area of a Semicircle\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-semi-circle\" aria-label=\"More on Area of a Semicircle\">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-23501","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\/23501","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=23501"}],"version-history":[{"count":22,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23501\/revisions"}],"predecessor-version":[{"id":39896,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23501\/revisions\/39896"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=23501"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=23501"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=23501"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}