{"id":26332,"date":"2023-03-14T16:08:24","date_gmt":"2023-03-14T16:08:24","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26332"},"modified":"2024-02-05T09:09:56","modified_gmt":"2024-02-05T09:09:56","slug":"surface-area-of-pyramid-definition-formula-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-pyramid","title":{"rendered":"Surface Area of Pyramid: Definition, Formula, Examples"},"content":{"rendered":"<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-4dc65d6c-4163-4c3a-8f94-cdfb98d37035\" 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\/surface-area-of-pyramid#0-what-is-the-surface-area-of-a-pyramid>What Is the Surface Area of a Pyramid?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-pyramid#1-surface-area-of-a-pyramid-formula>Surface Area of a Pyramid Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-pyramid#6-surface-area-of-a-pyramid-with-altitude>Surface Area of a Pyramid with Altitude<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-pyramid#8-solved-examples-on-surface-area-of-pyramid>Solved Examples on Surface Area of Pyramid<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-pyramid#9-practice-problems-on-surface-area-of-pyramid>Practice Problems on Surface Area of Pyramid<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-pyramid#10-frequently-asked-questions-on-surface-area-of-pyramid>Frequently Asked Questions on Surface Area of Pyramid<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<p class=\"eplus-wrapper\"><strong>A pyramid is a three-dimensional structure having a polygon as its base and triangular lateral faces<\/strong>. <strong>Surface area of a pyramid is simply the sum of all its faces. The pyramids are named after the polygon at its base.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here\u2019s an image showing a rectangular pyramid and a triangular pyramid.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"452\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/examples-of-pyramids.png\" alt=\"Examples of pyramids\" class=\"wp-image-37286\" title=\"Examples of pyramids\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/examples-of-pyramids.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/examples-of-pyramids-300x219.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-surface-area-of-a-pyramid\">What Is the Surface Area of a Pyramid?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The surface area of a pyramid is the sum of the areas of all faces of the pyramid. Surface area is measured in squared units such as cm<sup>2<\/sup>, m<sup>2<\/sup>, in<sup>2<\/sup>, etc.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since, all the faces of a pyramid are triangles except for the base, the surface area is calculated by finding the area of the triangular faces along with the area of the base.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example:<\/strong> If you open up the square pyramid, its net and individual faces will look like this:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"479\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/surface-area-of-a-pyramid-example-using-net.png\" alt=\"Surface area of a pyramid example using net\" class=\"wp-image-37287\" title=\"Surface area of a pyramid example using net\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/surface-area-of-a-pyramid-example-using-net.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/surface-area-of-a-pyramid-example-using-net-300x232.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">In order to find its surface area, we will add up the areas of four triangular faces and the area of the square at its base.<\/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-surface-area-of-a-pyramid-formula\">Surface Area of a Pyramid Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">There are two types of surface areas.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Total Surface Area (TSA):<\/strong> It refers to the area of all the faces of a pyramid.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The Total Surface area of any pyramid = Area of base + Area of each of the lateral faces<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Lateral Surface Area (LSA):<\/strong> It refers to the area of the lateral faces<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The Lateral Surface Area of pyramid (LSA) = Area of the triangular lateral faces<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong><em>Important Note:<\/em><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The surface area of a regular pyramid $=$ Base Area $+ \\frac{1}{2} Ps$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Where, P: Perimeter of the base and s: slant height<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s take a look at the formulas for the surface area of different pyramids.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"2-triangular-pyramid\">Triangular Pyramid<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"564\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/surface-area-of-triangular-pyramid.png\" alt=\"Surface area of triangular pyramid\" class=\"wp-image-37288\" title=\"Surface area of triangular pyramid\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/surface-area-of-triangular-pyramid.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/surface-area-of-triangular-pyramid-300x273.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Surface area of triangular pyramid $=$ Base area $+ LSA = \\frac{1}{2} ab + \\frac{3}{2}bs$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, b: side of the base triangle<\/p>\n\n\n\n<p class=\"eplus-wrapper\">a: height of the base triangle<\/p>\n\n\n\n<p class=\"eplus-wrapper\">s: slant height<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"3-square-pyramid\">Square Pyramid<\/h3>\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\/2024\/01\/square-pyramid-1.png\" alt=\"Square pyramid\" class=\"wp-image-37289\" title=\"Square pyramid\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/square-pyramid-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/square-pyramid-1-300x250.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Surface area of a square pyramid $=$ Area of the base $+ LSA = b^2 + 2bs$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, b: side of the base-square<\/p>\n\n\n\n<p class=\"eplus-wrapper\">s: slant height<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-fractions-using-area-models.jpeg\" alt=\"Add Fractions using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-like-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-like-fractions-using-area-models.jpeg\" alt=\"Add Like Fractions using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-mixed-numbers-and-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" 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 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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 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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=\"4-proof-of-surface-area-of-pyramid-formula\">Proof of Surface Area of Pyramid Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let us look at the net of a square pyramid.&nbsp;<\/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\/2024\/01\/net-of-a-square-pyramid.png\" alt=\"Net of a square pyramid\" class=\"wp-image-37290\" title=\"Net of a square pyramid\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/net-of-a-square-pyramid.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/net-of-a-square-pyramid-300x222.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The area of the square at the center (base of the pyramid $= (side)^2 = s^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of one lateral face $=$ area of a triangle $= 12 \\times base \\times height<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, base = side of the square = s and height = slant height (l)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of triangle $= \\frac{1}{2} \\times side \\times l$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of 4 of these triangles $= 4 \\times \\frac{1}{2} \\times s \\times l = 2 \\times side \\times l$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Total surface area $= 2 \\times side \\times l +(side)^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the formula for the surface area of a square pyramid is $2\\; sl + s^2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$s =$ side of the base<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$l =$ slant height<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, proved.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-how-to-find-the-surface-area-of-a-pyramid\">How to Find the Surface Area of a Pyramid<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1:<\/strong> First of all find the measurement of the base. If it is a rectangle, then we find the length and width. If it is a square, then we find the length of the side.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2:<\/strong> Find the area of the base. This area is known as \u201cA.\u201d<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3:<\/strong> Then we measure the slant height. This distance is known as \u201cl.\u201d<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4:<\/strong> Now we put the values in the surface area of a pyramid formula.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-surface-area-of-a-pyramid-with-altitude\">Surface Area of a Pyramid with Altitude<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The surface area of the pyramid can also be calculated if the altitude base length is given.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"490\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/surface-area-using-altitude.png\" alt=\"Surface area using altitude\" class=\"wp-image-37291\" title=\"Surface area using altitude\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/surface-area-using-altitude.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/surface-area-using-altitude-300x237.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The slant height can be calculated using the Pythagoras theorem as<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(slant\\; height)^2 = (\\frac{a}{2})^2 + (Altitude)^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$s^2 = (\\frac{a}{2})^2 + h^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Using this value, the surface area of the pyramid can be calculated.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned about the surface area of square pyramids. We saw the formula and ways to calculate the surface area of square pyramids. Let\u2019s now solve a few examples on the surface area of a pyramid and do some practice problems to understand it better.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-solved-examples-on-surface-area-of-pyramid\">Solved Examples on Surface Area of Pyramid<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. A square pyramid has base dimensions of <\/strong>$75\\; ft \\times 75\\; ft$<strong> and its slant height is around 500 ft. Calculate its surface area.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Base Area $= 75 \\times 75 = 562,5$ square feet.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The slant height of the pyramid is $l = 50\\; ft$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Surface area of pyramid $= (2 \\times s \\times l) + s^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$=(2 \\times 75 \\times 50) + 5625$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 7500 + 5625$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$=13125\\; sq.\\; ft$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. The base of a square pyramid has dimensions $<\/strong>10\\; units \\times 10\\; units$<strong> and the slant height is 4 units. What is the area of the canvas she will require to build the tent?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The base area $=$ Area of a square $= A = 10 \\times 5 = 50$ square units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The slant height of the tent is $l = 4$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of canvas to build the tent using the surface area of pyramid formula is,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Surface area of pyramid $= 2 \\times s \\times l + Base Area$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= (2 \\times 10 \\times 4) + 50$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 80 + 100$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 180\\; sq.\\; units$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. For the triangular pyramid, the side length of the base is 7 cm and height of the base is 6 cm. Find its surface area if the slant height of the pyramid is 16 cm.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given the side length of the base $= 7\\; cm,\\; height = 6\\; cm$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slant height $l = 16\\; cm$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Surface area of pyramid $= \\frac{1}{2} \\times b \\times h + \\frac{3}{2} \\times b \\times l$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Where, s = side of the base<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$l =$ slant height,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$b =$ base length,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$h =$ height of the base<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, surface area of pyramid $= (\\frac{1}{2} \\times 7 \\times 6) + (\\frac{3}{2} \\times 7 \\times 16)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 21\\; cm^2 + 168\\; cm^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 189\\; cm^2$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The surface area of the given pyramid is $189\\; cm^2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. What is the slant height of a pyramid if the surface area is <\/strong>$560\\; in^2$<strong> and side length is 14 inches.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Surface area of a pyramid $= 560\\; in^2$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Side length $s = 14$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Surface area of pyramid $= (2 \\times s \\times l) + s^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 560 = 2 \\times 14 \\times l + 14^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 560 = 28\\;l + 196$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 28\\;l = 560\\;-\\;196$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow l = 364\/28$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow l = 13$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The slant height of the given pyramid is 13 inches.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-practice-problems-on-surface-area-of-pyramid\">Practice Problems on Surface Area of Pyramid<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Surface Area of Pyramid: Definition, Formula, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">A square pyramid has ___ faces.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5<\/div><div class=\"spq_answer_block\" data-value=\"1\">6<\/div><div class=\"spq_answer_block\" data-value=\"2\">4<\/div><div class=\"spq_answer_block\" data-value=\"3\">3<\/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: 5<br\/>A square pyramid has 5 faces: 1 square base and 4 lateral triangular faces.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The base of a square pyramid has dimensions$- 15\\text{units}\\times15\\text{units}$ and the slant height is 5 units. What is the area of the canvas he will need to build the dollhouse?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">300 sq. units<\/div><div class=\"spq_answer_block\" data-value=\"1\">325 sq. units<\/div><div class=\"spq_answer_block\" data-value=\"2\">350 sq. units<\/div><div class=\"spq_answer_block\" data-value=\"3\">375 sq. units<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 375 sq. units<br\/>Base area $= A = 15\\times15 = 225$ square units.<br>\r\nThe slant height of the doll house is $l = 5$ units.<br>\r\nSurface area of pyramid$= 2\\times s \\times l + s^2$<br>\r\n$=2\\times15\\times5 + 225$<br>\r\n$=150 + 225$<br>\r\n$= 375$ sq. units<br>\r\nThe area of canvas to build the dollhouse $= 375$ sq. units<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the slant height of the side of the base if the surface area is $1200$ in$^{2}$ and side length is 20 inches.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">18 inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">20 inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">22 inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">28 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: 20 inches<br\/>Given the surface area $= 1200$ in$^{2}$ and<br>\r\nAnd the side length $s = 20$ inches<br>\r\nSurface area of pyramid $= 2 \\times s \\times l + s^{2}$<br>\r\n$\\Rightarrow$ $1200 = 2 \\times 20 \\times l + 202$<br>\r\n$\\Rightarrow$ $200 = 40 \\times l + 400$<br>\r\n$\\Rightarrow$ $40 \\times l = 1200 - 400$<br>\r\n$\\Rightarrow$ $l = \\frac{800}{40}$<br>\r\n$\\Rightarrow$ $l = 20$<br>\r\nThe slant height of the given pyramid is 20 inches.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Surface Area of Pyramid: Definition, Formula, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Surface Area of Pyramid\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A square pyramid has ___ faces.\",\n                    \"text\": \"A square pyramid has ___ faces.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A square pyramid has 5 faces: 1 square base and 4 lateral triangular faces.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A square pyramid has 5 faces: 1 square base and 4 lateral triangular faces.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A square pyramid has 5 faces: 1 square base and 4 lateral triangular faces.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A square pyramid has 5 faces: 1 square base and 4 lateral triangular faces.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A square pyramid has 5 faces: 1 square base and 4 lateral triangular faces.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A square pyramid has 5 faces: 1 square base and 4 lateral triangular faces.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The base of a square pyramid has dimensions$$- 15\\\\text{units}\\\\times15\\\\text{units}$$ and the slant height is 5 units. What is the area of the canvas he will need to build the dollhouse?\",\n                    \"text\": \"The base of a square pyramid has dimensions$$- 15\\\\text{units}\\\\times15\\\\text{units}$$ and the slant height is 5 units. What is the area of the canvas he will need to build the dollhouse?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Base area $$= A = 15\\\\times15 = 225$$ square units.<br>\r\nThe slant height of the doll house is $$l = 5$$ units.<br>\r\nSurface area of pyramid$$= 2\\\\times s \\\\times l + s^2$$<br>\r\n$$=2\\\\times15\\\\times5 + 225$$<br>\r\n$$=150 + 225$$<br>\r\n$$= 375$$ sq. units<br>\r\nThe area of canvas to build the dollhouse $$= 375$$ sq. units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"300 sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base area $$= A = 15\\\\times15 = 225$$ square units.<br>\r\nThe slant height of the doll house is $$l = 5$$ units.<br>\r\nSurface area of pyramid$$= 2\\\\times s \\\\times l + s^2$$<br>\r\n$$=2\\\\times15\\\\times5 + 225$$<br>\r\n$$=150 + 225$$<br>\r\n$$= 375$$ sq. units<br>\r\nThe area of canvas to build the dollhouse $$= 375$$ sq. units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"325 sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base area $$= A = 15\\\\times15 = 225$$ square units.<br>\r\nThe slant height of the doll house is $$l = 5$$ units.<br>\r\nSurface area of pyramid$$= 2\\\\times s \\\\times l + s^2$$<br>\r\n$$=2\\\\times15\\\\times5 + 225$$<br>\r\n$$=150 + 225$$<br>\r\n$$= 375$$ sq. units<br>\r\nThe area of canvas to build the dollhouse $$= 375$$ sq. units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"350 sq. units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base area $$= A = 15\\\\times15 = 225$$ square units.<br>\r\nThe slant height of the doll house is $$l = 5$$ units.<br>\r\nSurface area of pyramid$$= 2\\\\times s \\\\times l + s^2$$<br>\r\n$$=2\\\\times15\\\\times5 + 225$$<br>\r\n$$=150 + 225$$<br>\r\n$$= 375$$ sq. units<br>\r\nThe area of canvas to build the dollhouse $$= 375$$ sq. units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"375 sq. units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Base area $$= A = 15\\\\times15 = 225$$ square units.<br>\r\nThe slant height of the doll house is $$l = 5$$ units.<br>\r\nSurface area of pyramid$$= 2\\\\times s \\\\times l + s^2$$<br>\r\n$$=2\\\\times15\\\\times5 + 225$$<br>\r\n$$=150 + 225$$<br>\r\n$$= 375$$ sq. units<br>\r\nThe area of canvas to build the dollhouse $$= 375$$ sq. units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Base area $$= A = 15\\\\times15 = 225$$ square units.<br>\r\nThe slant height of the doll house is $$l = 5$$ units.<br>\r\nSurface area of pyramid$$= 2\\\\times s \\\\times l + s^2$$<br>\r\n$$=2\\\\times15\\\\times5 + 225$$<br>\r\n$$=150 + 225$$<br>\r\n$$= 375$$ sq. units<br>\r\nThe area of canvas to build the dollhouse $$= 375$$ sq. units\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the slant height of the side of the base if the surface area is $$1200$$ in$$^{2}$$ and side length is 20 inches.\",\n                    \"text\": \"What is the slant height of the side of the base if the surface area is $$1200$$ in$$^{2}$$ and side length is 20 inches.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Given the surface area $$= 1200$$ in$$^{2}$$ and<br>\r\nAnd the side length $$s = 20$$ inches<br>\r\nSurface area of pyramid $$= 2 \\\\times s \\\\times l + s^{2}$$<br>\r\n$$\\\\Rightarrow$$ $$1200 = 2 \\\\times 20 \\\\times l + 202$$<br>\r\n$$\\\\Rightarrow$$ $$200 = 40 \\\\times l + 400$$<br>\r\n$$\\\\Rightarrow$$ $$40 \\\\times l = 1200 - 400$$<br>\r\n$$\\\\Rightarrow$$ $$l = \\\\frac{800}{40}$$<br>\r\n$$\\\\Rightarrow$$ $$l = 20$$<br>\r\nThe slant height of the given pyramid is 20 inches.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"18 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given the surface area $$= 1200$$ in$$^{2}$$ and<br>\r\nAnd the side length $$s = 20$$ inches<br>\r\nSurface area of pyramid $$= 2 \\\\times s \\\\times l + s^{2}$$<br>\r\n$$\\\\Rightarrow$$ $$1200 = 2 \\\\times 20 \\\\times l + 202$$<br>\r\n$$\\\\Rightarrow$$ $$200 = 40 \\\\times l + 400$$<br>\r\n$$\\\\Rightarrow$$ $$40 \\\\times l = 1200 - 400$$<br>\r\n$$\\\\Rightarrow$$ $$l = \\\\frac{800}{40}$$<br>\r\n$$\\\\Rightarrow$$ $$l = 20$$<br>\r\nThe slant height of the given pyramid is 20 inches.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"22 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given the surface area $$= 1200$$ in$$^{2}$$ and<br>\r\nAnd the side length $$s = 20$$ inches<br>\r\nSurface area of pyramid $$= 2 \\\\times s \\\\times l + s^{2}$$<br>\r\n$$\\\\Rightarrow$$ $$1200 = 2 \\\\times 20 \\\\times l + 202$$<br>\r\n$$\\\\Rightarrow$$ $$200 = 40 \\\\times l + 400$$<br>\r\n$$\\\\Rightarrow$$ $$40 \\\\times l = 1200 - 400$$<br>\r\n$$\\\\Rightarrow$$ $$l = \\\\frac{800}{40}$$<br>\r\n$$\\\\Rightarrow$$ $$l = 20$$<br>\r\nThe slant height of the given pyramid is 20 inches.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"28 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given the surface area $$= 1200$$ in$$^{2}$$ and<br>\r\nAnd the side length $$s = 20$$ inches<br>\r\nSurface area of pyramid $$= 2 \\\\times s \\\\times l + s^{2}$$<br>\r\n$$\\\\Rightarrow$$ $$1200 = 2 \\\\times 20 \\\\times l + 202$$<br>\r\n$$\\\\Rightarrow$$ $$200 = 40 \\\\times l + 400$$<br>\r\n$$\\\\Rightarrow$$ $$40 \\\\times l = 1200 - 400$$<br>\r\n$$\\\\Rightarrow$$ $$l = \\\\frac{800}{40}$$<br>\r\n$$\\\\Rightarrow$$ $$l = 20$$<br>\r\nThe slant height of the given pyramid is 20 inches.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"20 inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Given the surface area $$= 1200$$ in$$^{2}$$ and<br>\r\nAnd the side length $$s = 20$$ inches<br>\r\nSurface area of pyramid $$= 2 \\\\times s \\\\times l + s^{2}$$<br>\r\n$$\\\\Rightarrow$$ $$1200 = 2 \\\\times 20 \\\\times l + 202$$<br>\r\n$$\\\\Rightarrow$$ $$200 = 40 \\\\times l + 400$$<br>\r\n$$\\\\Rightarrow$$ $$40 \\\\times l = 1200 - 400$$<br>\r\n$$\\\\Rightarrow$$ $$l = \\\\frac{800}{40}$$<br>\r\n$$\\\\Rightarrow$$ $$l = 20$$<br>\r\nThe slant height of the given pyramid is 20 inches.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Given the surface area $$= 1200$$ in$$^{2}$$ and<br>\r\nAnd the side length $$s = 20$$ inches<br>\r\nSurface area of pyramid $$= 2 \\\\times s \\\\times l + s^{2}$$<br>\r\n$$\\\\Rightarrow$$ $$1200 = 2 \\\\times 20 \\\\times l + 202$$<br>\r\n$$\\\\Rightarrow$$ $$200 = 40 \\\\times l + 400$$<br>\r\n$$\\\\Rightarrow$$ $$40 \\\\times l = 1200 - 400$$<br>\r\n$$\\\\Rightarrow$$ $$l = \\\\frac{800}{40}$$<br>\r\n$$\\\\Rightarrow$$ $$l = 20$$<br>\r\nThe slant height of the given pyramid is 20 inches.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-frequently-asked-questions-on-surface-area-of-pyramid\">Frequently Asked Questions on Surface Area of Pyramid<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-94bac9c3-f241-4cc8-be5d-eb8915e0b260\" 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-0-94bac9c3-f241-4cc8-be5d-eb8915e0b260\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-94bac9c3-f241-4cc8-be5d-eb8915e0b260\"><strong>What is the volume of a pyramid?<\/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-0-94bac9c3-f241-4cc8-be5d-eb8915e0b260\">\n\n<p class=\"eplus-wrapper\">The volume of the pyramid with the area of the base \u201cA\u201d and the height \u201ch\u201d is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Volume $= \\frac{1}{3} \\times A \\times h$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-94bac9c3-f241-4cc8-be5d-eb8915e0b260\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-94bac9c3-f241-4cc8-be5d-eb8915e0b260\"><strong>What is a prism?<\/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-1-94bac9c3-f241-4cc8-be5d-eb8915e0b260\">\n\n<p class=\"eplus-wrapper\">A prism is a solid object with ends that are parallel and of the same size and shape, and with sides whose opposite edges are equal and parallel.<\/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-2-94bac9c3-f241-4cc8-be5d-eb8915e0b260\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-94bac9c3-f241-4cc8-be5d-eb8915e0b260\"><strong>What is the regular pyramid?<\/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-2-94bac9c3-f241-4cc8-be5d-eb8915e0b260\">\n\n<p class=\"eplus-wrapper\">A regular pyramid is a pyramid whose base is a regular polygon and all the lateral edges are also equal in length.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>A pyramid is a three-dimensional structure having a polygon as its base and triangular lateral faces. Surface area of a pyramid is simply the sum of all its faces. The pyramids are named after the polygon at its base. Here\u2019s an image showing a rectangular pyramid and a triangular pyramid. What Is the Surface Area &#8230; <a title=\"Surface Area of Pyramid: Definition, Formula, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-pyramid\" aria-label=\"More on Surface Area of Pyramid: Definition, Formula, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-26332","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\/26332","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=26332"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26332\/revisions"}],"predecessor-version":[{"id":39895,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26332\/revisions\/39895"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26332"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26332"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}