{"id":27787,"date":"2023-04-23T07:50:28","date_gmt":"2023-04-23T07:50:28","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=27787"},"modified":"2024-02-05T15:24:23","modified_gmt":"2024-02-05T15:24:23","slug":"area-of-a-pentagon-definition-formula-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-pentagon","title":{"rendered":"Area of a Pentagon &#8211; Definition, Formula,\u00a0 Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-77a16cb9-e70a-419c-a0a6-a3f433af7e64\" 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-pentagon#0-what-is-the-area-of-a-pentagon>What Is the Area of a Pentagon?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-pentagon#1-area-of-a-pentagon-formula->Area of a Pentagon Formula&nbsp;<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-pentagon#2-how-to-find-the-area-of-a-pentagon>How to Find the Area of a Pentagon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-pentagon#7-solved-examples-on-area-of-pentagon>Solved Examples on Area of Pentagon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-pentagon#8-practice-problems-on-area-of-a-pentagon>Practice Problems on Area of a Pentagon<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-pentagon#9-frequently-asked-questions-on-area-of-a-pentagon>Frequently Asked Questions on Area of a Pentagon<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-area-of-a-pentagon\">What Is the Area of a Pentagon?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A pentagon is a polygon having five sides and 5 angles. The Greek word \u201cpenta\u201d means \u201cfive\u201d and \u201cgon\u201d means \u201cangles.\u201d<strong> The area of a pentagon is the region bounded by the five sides of the pentagon.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the image below, we can see that the area of the pentagon is shaded in black color.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"335\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/pentagon-and-area-of-pentagon.png\" alt=\"Pentagon and area of pentagon\" class=\"wp-image-33797\" title=\"Pentagon and area of pentagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/pentagon-and-area-of-pentagon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/pentagon-and-area-of-pentagon-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>The area of a pentagon is the region that is enclosed within the five sides of a pentagon.<\/strong> There are many methods for calculating the area of a pentagon depending upon the dimensions that are known to us. The type of pentagon also plays a major role in calculating the area.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>The area of a regular pentagon can be calculated with the help of a fixed formula, <\/strong>but if we have an irregular pentagon, then we need to break it down into multiple different polygons and sum up their areas to get the area of the pentagon.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The area of a pentagon is expressed in \u201csquare units,\u201d like $cm^2,\\; in^2,\\; m^2,\\; ft^2$, etc.&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\/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 class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-area-of-shapes-using-unit-shapes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_unit_square_side_length_pt.png\" alt=\"Find the Area of Shapes Using Unit Shapes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Area of Shapes Using Unit Shapes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-area-of-a-pentagon-formula-\">Area of a Pentagon Formula&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">There are many methods and formulas to find the area of a pentagon and it varies according to the type of the pentagon. The most commonly used formula for the area of a pentagon is<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area\\; of\\; a\\; Pentagon = \\frac{1}{2} \\times Perimeter \\times Apothem$<strong><br><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong> &nbsp;  &nbsp; &nbsp; &nbsp; &nbsp; <\/strong>$= \\frac{1}{2} \\times p \\times a$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u201c<strong>p<\/strong>\u201d is the perimeter of the pentagon.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u201c<strong>a<\/strong>\u201d is the apothem of the pentagon.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Note:<\/strong> An apothem of a regular polygon is a perpendicular drawn from the center to the midpoint of any of its sides.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"535\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/apothem-of-a-pentagon.png\" alt=\"Apothem of a pentagon\" class=\"wp-image-33798\" title=\"Apothem of a pentagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/apothem-of-a-pentagon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/apothem-of-a-pentagon-300x259.png 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\/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\" 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>\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            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Pentagon with Apothem<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Area of Irregular Pentagon<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-area-of-regular-pentagon\">Area of Regular Pentagon<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A regular pentagon is a pentagon in which all the sides are equal and all angles are of equal measures. The area of a regular pentagon can be calculated only if the side length \u201cs\u201d is known to us.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula used to find the area of a regular pentagon is:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of regular pentagon$= \\frac{1}{4}\\sqrt{5 ( 5 + 2\\sqrt{5} )}\\;s^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u201cs\u201d : the length of the side of the regular pentagon.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example: Find the area of a regular pentagon whose side is 5 units.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of regular pentagon $= \\frac{1}{4}\\sqrt{5( 5 + 2\\sqrt{5})}\\;s^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given $s = 5$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">After substituting the value of $s = 5$, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{1}{4}\\sqrt{5 ( 5 + 2\\sqrt{5})}\\;s^2 = \\frac{1}{4}\\sqrt{25 + 105)} \\times 25 = 43.011$ square units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Note<\/strong>:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The term $\\frac{1}{4}\\sqrt{5 ( 5 + 2\\sqrt{5})}$ in the formula equals 1.7204774006.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find an estimate, we can use $\\frac{1}{4}\\sqrt{5(5+2\\sqrt{5})} \\simeq 1.72$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We may not get accuracy till the last decimal point, but the answer will be very close to the actual result.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the formula can be written as:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of a regular pentagon with side \u201cs\u201d $= 1.72\\; s^2$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-area-of-pentagon-with-apothem\">Area of Pentagon with Apothem<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we know the side and apothem of a pentagon, the area of a pentagon can be calculated by the formula<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of regular polygon$= \\frac{1}{2} \\times Perimeter\\; of\\; polygon\\; \\times Apothem$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of regular pentagon$= \\frac{1}{2} \\times p \\times a$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">where \u201cp\u201d is the perimeter of the pentagon and \u201ca\u201d is the apothem of the pentagon.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example: Find the area of a regular pentagon whose side length is 12 units and the length of apothem is 3 units.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution: <\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$s = 12$ units and $a = 3$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of pentagon $= 5 \\times side\\; length\\; = 5 \\times 12 = 60$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of the pentagon, $A = \\frac{1}{2} \\times p \\times a$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substitute $p = 60,\\; a = 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow A = \\frac{1}{2} \\times 60 \\times 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow A = 90$ square units<br><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the area of the pentagon is 90 square units.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-area-of-an-irregular-pentagon\">Area of an Irregular Pentagon<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we have an irregular pentagon, we can calculate its area by dividing the pentagon into smaller polygons such as rectangles, triangles. We calculate the area of these polygons and add them together to get the area of the pentagon.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example: Find the area of a given irregular pentagon.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"395\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/irregular-pentagon-with-dimensions-given.png\" alt=\"Irregular pentagon with dimensions given\" class=\"wp-image-33800\" title=\"Irregular pentagon with dimensions given\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/irregular-pentagon-with-dimensions-given.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/irregular-pentagon-with-dimensions-given-300x191.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> The given pentagon can be divided into a triangle and a rectangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Area of triangle<\/strong> $= \\frac{1}{2} \\times Base \\times Height$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{1}{2}\\times 12 \\times 4$ <\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 24$ square feet<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Area of rectangle<\/strong> $= Length\\times Width$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 12 \\times 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 96$ square feet<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Area of given irregular pentagon<\/strong> $= Area\\; of\\; triangle + Area\\; of\\; rectangle$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 24 + 96$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 120$ square feet<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Facts about Area of Pentagon<\/strong><\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The sum of all the interior angles of a regular pentagon is equal to $540^\\circ$.<\/li>\n<\/ol>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">In a regular pentagon, each interior angle is equal to 108\u00b0 and each exterior angle is equal to $72^\\circ$.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned how to find the area of a pentagon. We discussed three methods to find the area of the pentagon. Let us 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-pentagon\">Solved Examples on Area of Pentagon<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Find the area of the regular pentagon with side <\/strong>$= 8$<strong> feet?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the formula to calculate the area of a regular pentagon is,<br><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of regular pentagon $= \\frac{1}{4} \\sqrt{5 (5 + 2\\sqrt{5})}\\;s^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">side $(s) = 8\\; ft$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Putting the value in the above formula:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$Area = \\frac{1}{4}\\sqrt{5 (5 + 2\\sqrt{5})}\\;s^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; $= \\frac{1}{4} \\times 64 \\times 6.882$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 110.112\\;ft^2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><br>Therefore, the area of the pentagon of side 8 is $110.112\\;ft^2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. Calculate the area of a regular pentagon given that the length of the side of the pentagon is 10 feet and the length of the apothem is 7 feet.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given, $s = 10$ and $a = 7$ .<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula to calculate the area of a pentagon with apothem is:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of pentagon $= \\frac{1}{2} \\times perimeter \\times apothem$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us calculate the perimeter of the pentagon.<br><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of the pentagon $= 5 \\times side length = 5 \\times 10 = 50$ feet&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, let us put these values in the above formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of pentagon $= \\frac{1}{2} \\times p \\times a$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;$\\Rightarrow A = \\frac{1}{2} \\times 50 \\times 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;$\\Rightarrow A = 175\\;feet^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the area of the pentagon is 175 square feet.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Find the length of the apothem of the pentagon if the area of a pentagon is 600 square feet and side length is 12 feet.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of pentagon $= 600$ units feet&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$s = 12$ feet<br><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of pentagon$= p = 5 \\times side\\; length = 5 \\times 12 = 60$ units&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Using the formula for the area of a pentagon,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of pentagon $= \\frac{1}{2} \\times p \\times a$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow  600 = \\frac{1}{2} \\times 60 \\times a$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow  a = \\frac{600}{30}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow a = 20$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the length of the apothem is 20 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Find the area of the given pentagon.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"248\" height=\"288\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/an-irregular-pentagon.png\" alt=\"An irregular pentagon\" class=\"wp-image-33801\" title=\"An irregular pentagon\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Divide the pentagon into a rectangle and a triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"248\" height=\"288\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/irregular-pentagon-divided-into-smaller-polygons.png\" alt=\"Irregular pentagon divided into smaller polygons\" class=\"wp-image-33802\" title=\"Irregular pentagon divided into smaller polygons\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of triangle $= \\frac{1}{2} Base \\times Height = \\frac{1}{2}\\times10\\times3 = 15$ square feet<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of rectangle $= Length \\times Width = 10\\times12 = 120$ square feet<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of given pentagon $= Area \\;of \\;triangle + Area\\; of\\; rectangle$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; $= 15 + 120$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp; &nbsp; &nbsp; $= 135$ square feet<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-practice-problems-on-area-of-a-pentagon\">Practice Problems on Area of a Pentagon<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Area of a Pentagon - Definition, Formula,\u00a0 Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The area of a pentagon can be calculated using<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">perimeter alone<\/div><div class=\"spq_answer_block\" data-value=\"1\">side<\/div><div class=\"spq_answer_block\" data-value=\"2\">perimeter and apothem<\/div><div class=\"spq_answer_block\" data-value=\"3\">apothem alone<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: perimeter and apothem<br\/>Area of pentagon is given by $12 \\times perimeter \\times apothem$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Perimeter of the pentagon $= 75$ feet<br>Length of the apothem $= 10$ feet<br>Find the area.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$335\\; feet^2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$325\\; feet^2$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$375\\; feet^2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$385\\; feet^2$<\/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: $375\\; feet^2$<br\/>Here, $p = 75$ feet and $a = 10$ feet<br>\r\nArea of pentagon$= 12 \\times perimeter \\times apothem$<br>\r\n$\\Rightarrow  A = 12 \\times 75 \\times 10$<br>\r\n$Rightarrow A = 375\\;feet^2$<\/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\">What is the area of the given irregular pentagon?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">120 sq. ft<\/div><div class=\"spq_answer_block\" data-value=\"1\">135 sq. ft<\/div><div class=\"spq_answer_block\" data-value=\"2\">140 sq. ft<\/div><div class=\"spq_answer_block\" data-value=\"3\">150 sq. ft<\/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: 150 sq. ft<br\/>Height of the triangle $= 18\\;in\\;-\\;12\\;in = 6\\;in$<br>\r\nArea of triangle $= \\frac{1}{2}$ BaseHeight $= \\frac{1}{2}\\times10\\times6 = 30$ square feet<br>\r\nArea of rectangle $= Length \\times Width = 10\\times12 = 120$ square feet<br>\r\nArea of given irregular pentagon $= Area\\; of \\;triangle + Area\\; of\\; rectangle$<br>\t      \t\t  \r\n$= 30 + 120$<br>\r\n$= 150$ square feet<\/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 Pentagon - Definition, Formula,\u00a0 Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Area of a Pentagon\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    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          \"@type\": \"Comment\",\n                                    \"text\": \"Area of pentagon is given by $$12 \\\\times perimeter \\\\times apothem$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"perimeter and apothem\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Area of pentagon is given by $$12 \\\\times perimeter \\\\times apothem$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Area of pentagon is given by $$12 \\\\times perimeter \\\\times apothem$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Perimeter of the pentagon $$= 75$$ feet<br>Length of the apothem $$= 10$$ feet<br>Find the area.\",\n                    \"text\": \"Perimeter of the pentagon $$= 75$$ feet<br>Length of the apothem $$= 10$$ feet<br>Find the area.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Here, $$p = 75$$ feet and $$a = 10$$ feet<br>\r\nArea of pentagon$$= 12 \\\\times perimeter \\\\times apothem$$<br>\r\n$$\\\\Rightarrow  A = 12 \\\\times 75 \\\\times 10$$<br>\r\n$$Rightarrow A = 375\\\\;feet^2$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$335\\\\; feet^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Here, $$p = 75$$ feet and $$a = 10$$ feet<br>\r\nArea of pentagon$$= 12 \\\\times perimeter \\\\times apothem$$<br>\r\n$$\\\\Rightarrow  A = 12 \\\\times 75 \\\\times 10$$<br>\r\n$$Rightarrow A = 375\\\\;feet^2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$325\\\\; feet^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Here, $$p = 75$$ feet and $$a = 10$$ feet<br>\r\nArea of pentagon$$= 12 \\\\times perimeter \\\\times apothem$$<br>\r\n$$\\\\Rightarrow  A = 12 \\\\times 75 \\\\times 10$$<br>\r\n$$Rightarrow A = 375\\\\;feet^2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$385\\\\; feet^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Here, $$p = 75$$ feet and $$a = 10$$ feet<br>\r\nArea of pentagon$$= 12 \\\\times perimeter \\\\times apothem$$<br>\r\n$$\\\\Rightarrow  A = 12 \\\\times 75 \\\\times 10$$<br>\r\n$$Rightarrow A = 375\\\\;feet^2$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$375\\\\; feet^2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Here, $$p = 75$$ feet and $$a = 10$$ feet<br>\r\nArea of pentagon$$= 12 \\\\times perimeter \\\\times apothem$$<br>\r\n$$\\\\Rightarrow  A = 12 \\\\times 75 \\\\times 10$$<br>\r\n$$Rightarrow A = 375\\\\;feet^2$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Here, $$p = 75$$ feet and $$a = 10$$ feet<br>\r\nArea of pentagon$$= 12 \\\\times perimeter \\\\times apothem$$<br>\r\n$$\\\\Rightarrow  A = 12 \\\\times 75 \\\\times 10$$<br>\r\n$$Rightarrow A = 375\\\\;feet^2$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the area of the given irregular pentagon?\",\n                    \"text\": \"What is the area of the given irregular pentagon?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Height of the triangle $$= 18\\\\;in\\\\;-\\\\;12\\\\;in = 6\\\\;in$$<br>\r\nArea of triangle $$= \\\\frac{1}{2}$$ BaseHeight $$= \\\\frac{1}{2}\\\\times10\\\\times6 = 30$$ square feet<br>\r\nArea of rectangle $$= Length \\\\times Width = 10\\\\times12 = 120$$ square feet<br>\r\nArea of given irregular pentagon $$= Area\\\\; of \\\\;triangle + Area\\\\; of\\\\; rectangle$$<br>\t      \t\t  \r\n$$= 30 + 120$$<br>\r\n$$= 150$$ square feet\"\n                    },\n                    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                          \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"135 sq. ft\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Height of the triangle $$= 18\\\\;in\\\\;-\\\\;12\\\\;in = 6\\\\;in$$<br>\r\nArea of triangle $$= \\\\frac{1}{2}$$ BaseHeight $$= \\\\frac{1}{2}\\\\times10\\\\times6 = 30$$ square feet<br>\r\nArea of rectangle $$= Length \\\\times Width = 10\\\\times12 = 120$$ square feet<br>\r\nArea of given irregular pentagon $$= Area\\\\; of \\\\;triangle + Area\\\\; of\\\\; rectangle$$<br>\t      \t\t  \r\n$$= 30 + 120$$<br>\r\n$$= 150$$ square feet\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"140 sq. ft\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Height of the triangle $$= 18\\\\;in\\\\;-\\\\;12\\\\;in = 6\\\\;in$$<br>\r\nArea of triangle $$= \\\\frac{1}{2}$$ BaseHeight $$= \\\\frac{1}{2}\\\\times10\\\\times6 = 30$$ square feet<br>\r\nArea of rectangle $$= Length \\\\times Width = 10\\\\times12 = 120$$ square feet<br>\r\nArea of given irregular pentagon $$= Area\\\\; of \\\\;triangle + Area\\\\; of\\\\; rectangle$$<br>\t      \t\t  \r\n$$= 30 + 120$$<br>\r\n$$= 150$$ square feet\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"150 sq. ft\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Height of the triangle $$= 18\\\\;in\\\\;-\\\\;12\\\\;in = 6\\\\;in$$<br>\r\nArea of triangle $$= \\\\frac{1}{2}$$ BaseHeight $$= \\\\frac{1}{2}\\\\times10\\\\times6 = 30$$ square feet<br>\r\nArea of rectangle $$= Length \\\\times Width = 10\\\\times12 = 120$$ square feet<br>\r\nArea of given irregular pentagon $$= Area\\\\; of \\\\;triangle + Area\\\\; of\\\\; rectangle$$<br>\t      \t\t  \r\n$$= 30 + 120$$<br>\r\n$$= 150$$ square feet\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Height of the triangle $$= 18\\\\;in\\\\;-\\\\;12\\\\;in = 6\\\\;in$$<br>\r\nArea of triangle $$= \\\\frac{1}{2}$$ BaseHeight $$= \\\\frac{1}{2}\\\\times10\\\\times6 = 30$$ square feet<br>\r\nArea of rectangle $$= Length \\\\times Width = 10\\\\times12 = 120$$ square feet<br>\r\nArea of given irregular pentagon $$= Area\\\\; of \\\\;triangle + Area\\\\; of\\\\; rectangle$$<br>\t      \t\t  \r\n$$= 30 + 120$$<br>\r\n$$= 150$$ square feet\"\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-pentagon\">Frequently Asked Questions on Area of a Pentagon<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-cd5c726f-46cd-415c-843b-5b66ae985af8\" 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-cd5c726f-46cd-415c-843b-5b66ae985af8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cd5c726f-46cd-415c-843b-5b66ae985af8\"><strong>What are the different types of pentagon?<\/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-cd5c726f-46cd-415c-843b-5b66ae985af8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">There are four types of pentagons:<br><\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Concave Pentagon<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Convex Pentagon<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Regular Pentagon<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Irregular Pentagon<\/li>\n<\/ol>\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-cd5c726f-46cd-415c-843b-5b66ae985af8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cd5c726f-46cd-415c-843b-5b66ae985af8\"><strong>What is a concave pentagon?<\/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-cd5c726f-46cd-415c-843b-5b66ae985af8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A pentagon in which there is at least one angle which is more than 180\u00b0 is known as a concave pentagon.<\/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-cd5c726f-46cd-415c-843b-5b66ae985af8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cd5c726f-46cd-415c-843b-5b66ae985af8\"><strong>What is a convex pentagon?<\/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-cd5c726f-46cd-415c-843b-5b66ae985af8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A pentagon in which every angle is less than 180\u00b0 is known as a convex pentagon.<\/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-cd5c726f-46cd-415c-843b-5b66ae985af8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cd5c726f-46cd-415c-843b-5b66ae985af8\"><strong>What is the name of a polygon with 6 sides?<\/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-cd5c726f-46cd-415c-843b-5b66ae985af8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A polygon with six sides is known as a hexagon.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Area of a Pentagon? A pentagon is a polygon having five sides and 5 angles. The Greek word \u201cpenta\u201d means \u201cfive\u201d and \u201cgon\u201d means \u201cangles.\u201d The area of a pentagon is the region bounded by the five sides of the pentagon. In the image below, we can see that the area of &#8230; <a title=\"Area of a Pentagon &#8211; Definition, Formula,\u00a0 Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-a-pentagon\" aria-label=\"More on Area of a Pentagon &#8211; Definition, Formula,\u00a0 Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-27787","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\/27787","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=27787"}],"version-history":[{"count":17,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27787\/revisions"}],"predecessor-version":[{"id":39914,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27787\/revisions\/39914"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=27787"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=27787"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=27787"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}