{"id":34199,"date":"2023-09-18T11:05:46","date_gmt":"2023-09-18T11:05:46","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=34199"},"modified":"2023-09-18T11:32:23","modified_gmt":"2023-09-18T11:32:23","slug":"surface-area-of-rectangular-prism-formula-facts-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-rectangular-prism","title":{"rendered":"Surface Area of Rectangular Prism &#8211; Formula, Facts, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-4d4ea759-3150-4c51-9a15-c248dbfc9473\" 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-rectangular-prism#0-what-is-the-surface-area-of-a-rectangular-prism>What Is the Surface Area of a Rectangular Prism?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-rectangular-prism#1-surface-area-of-rectangular-prism-formulas>Surface Area of Rectangular Prism: Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-rectangular-prism#3-how-to-find-the-surface-area-of-a-rectangular-prism>How to Find the Surface Area of a Rectangular Prism<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-rectangular-prism#5-solved-examples-on-surface-area-of-rectangular-prism>Solved Examples on Surface Area of Rectangular Prism<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-rectangular-prism#6-practice-problems-on-surface-area-of-rectangular-prism>Practice Problems on Surface Area of Rectangular Prism<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-rectangular-prism#7-frequently-asked-questions-on-the-surface-area-of-rectangular-prism>Frequently Asked Questions on the Surface Area of Rectangular Prism?<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-surface-area-of-a-rectangular-prism\">What Is the Surface Area of a Rectangular Prism?<\/h2>\n\n\n\n<p><strong>The total surface area of a rectangular prism (cuboid) is the total area covered by the surfaces (lateral and base) of a rectangular prism.<\/strong><\/p>\n\n\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/rectangular-prism\">rectangular prism<\/a> consists of 6 faces, each of which are rectangles. Its bases are congruent and parallel to each other. A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-rectangular-prism\">right rectangular prism<\/a> is also called a cuboid.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/rectangular-prism.png\" alt=\"Rectangular prism\" class=\"wp-image-34204\" title=\"Rectangular prism\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/rectangular-prism.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/rectangular-prism-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Note:<\/strong> Rectangular prisms are of two types: right rectangular prisms and oblique rectangular prisms. Throughout the article, the term \u2018rectangular prism\u2019 refers to \u2018right rectangular prism.\u2019<\/p>\n\n\n\n<p>The right rectangular prism has two parallel and congruent rectangular faces as its bases and four lateral faces, each one of them a rectangle. Also, the faces are perpendicular to each of its bases. The faces of an oblique rectangular prism are parallelograms.&nbsp;<\/p>\n\n\n\n<p>We can study the surface area of a rectangular prism as<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Base areas<\/strong>: The area of two rectangles at its base.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Lateral Surface Area<\/strong>: Lateral Surface Area of a Rectangular Prism is the area of the faces of the prism excluding the area of the base and the top. Suppose you have to paint the walls of the room. In such cases, we will exclude the area of ceiling and flooring.&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Total Surface Area<\/strong>: Total Surface Area of a rectangular prism is the area of all the faces of the prism including the area of the bases and the LSA.<\/li>\n<\/ul>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-to-find-the-area\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_find_area_pt.png\" alt=\"Add to Find the Area Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add to Find the Area Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-of-composite-figure\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_grannys_rescue_10_gm.png\" alt=\"Area of Composite Figure Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area of Composite Figure Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-with-unit-squares-and-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_unit_sq_side_length_pt.png\" alt=\"Area with Unit Squares and Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area with Unit Squares and Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-word-problems-on-product-of-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_real_life_prob_area_pt.png\" alt=\"Area Word Problems on Product of Fractions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area Word Problems on Product of Fractions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/build-the-area\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_grannys_rescue_3_4_5_gm.png\" alt=\"Build the Area Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Build the Area Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-objects-in-rectangular-arrays\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_hoppys_list_10_gm.png\" alt=\"Count Objects in Rectangular Arrays Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count Objects in Rectangular Arrays Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/determine-the-area-of-rectilinear-shapes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_rectilinear_shapes_pt.png\" alt=\"Determine the Area of Rectilinear Shapes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Determine the Area of Rectilinear Shapes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-area-by-multiplying-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_multi_side_length_1_pt.png\" alt=\"Find Area by Multiplying Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Area by Multiplying Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-area-in-square-units\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_grannys_rescue_1_2_gm.png\" alt=\"Find Area in Square Units Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Area in Square Units Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-area-by-multiplying-the-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_multiply_pt.png\" alt=\"Find the Area by Multiplying the Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Area by Multiplying the Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    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\" id=\"1-surface-area-of-rectangular-prism-formulas\">Surface Area of Rectangular Prism: Formulas<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"404\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/dimensions-of-rectangular-prism.png\" alt=\"Dimensions of rectangular prism\" class=\"wp-image-34205\" title=\"Dimensions of rectangular prism\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/dimensions-of-rectangular-prism.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/dimensions-of-rectangular-prism-300x195.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th><strong>Type of surface area<\/strong><\/th><th><strong>Description<\/strong><\/th><th><strong>Formula<\/strong><\/th><\/tr><\/thead><tbody><tr><td>Base Area<\/td><td>Area of the base<\/td><td>Area of one base = lw<br>Area of two bases = 2lw<\/td><\/tr><tr><td>Lateral Surface Area (LSA)<\/td><td>Area of the lateral sides (faces)<\/td><td>LSA = 2h(h + w)<\/td><\/tr><tr><td>Total Surface Area (TSA)<\/td><td>LSA + Area of two bases<\/td><td>TSA = 2wh + 2lh + 2lw<br>TSA = 2(lw + wh + lh)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Note:<\/strong> Breadth (b) and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/width\">width<\/a> (w) are two terms that are commonly used when discussing the measurements. They are often used interchangeably, especially when referring to the dimensions of a rectangular object.&nbsp;<\/p>\n\n\n\n<p>In this context, both terms describe the measurement of the shorter side that is perpendicular to the length and height. So, we can also define the formulas by replacing w by b. However, there may be subtle differences in the meaning of these terms in other contexts.<\/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 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 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-derivation-of-the-surface-area-of-rectangular-prism-formula\">Derivation of the Surface Area of Rectangular Prism Formula<\/h2>\n\n\n\n<p>Assume that l, w, h are the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/length\">length<\/a>, width, and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/height\">height<\/a> of the rectangular prism respectively.<\/p>\n\n\n\n<p>A rectangular box has 6 sides (faces): top\/bottom, front\/back, left side and right side.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"388\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/understanding-the-surface-area-of-rectangular-prism.png\" alt=\"Understanding the surface area of rectangular prism\" class=\"wp-image-34207\" title=\"Understanding the surface area of rectangular prism\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/understanding-the-surface-area-of-rectangular-prism.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/understanding-the-surface-area-of-rectangular-prism-300x188.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>There are two faces (front and back) with dimension l \u2715 h.<\/p>\n\n\n\n<p>Area of these two faces = 2(l \u2715 h)<\/p>\n\n\n\n<p>There are two faces (top and bottom ones) with dimension l \u2715 w.<\/p>\n\n\n\n<p>Area of these two faces = 2(l \u2715 w)<\/p>\n\n\n\n<p>There are two faces (left and right) with dimension w \u2715 h.<\/p>\n\n\n\n<p>Area of these two faces = 2(w \u2715 h)<\/p>\n\n\n\n<p>The Lateral Surface Area is the sum of the faces of a rectangular prism except the top and base.&nbsp;<\/p>\n\n\n\n<p>Lateral surface area of rectangular prism = lh + wh + lh + wh<\/p>\n\n\n\n<p>LSA =2lh + 2wh<\/p>\n\n\n\n<p>LSA = 2h(l + w)<\/p>\n\n\n\n<p>The total surface area is the sum of all the faces of a rectangular prism.<\/p>\n\n\n\n<p>Total Surface Area of rectangular prism = 2lw + 2wh + 2hl\u00a0\u00a0<\/p>\n\n\n\n<p>TSA = 2(lw + wh + hl)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-find-the-surface-area-of-a-rectangular-prism\">How to Find the Surface Area of a Rectangular Prism<\/h2>\n\n\n\n<p><strong>Step 1:<\/strong> Check if the dimensions of the rectangular prism are in the same units or not. If not, convert them into the same units.<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Once the dimensions are of the same units, understand whether you have to calculate the lateral surface area or the total surface area according to the given situation.&nbsp;<\/p>\n\n\n\n<p><strong>Step 3: <\/strong>Apply the formulas:&nbsp;<\/p>\n\n\n\n<p>&nbsp;lateral surface area = 2h(l + w)<\/p>\n\n\n\n<p>&nbsp;total surface area = 2(lw + wh + lh)&nbsp;<\/p>\n\n\n\n<p><strong>Example: <\/strong>Jasmine has to wrap a rectangular box of length 20 in, breadth 10 in and height 7 in. How much wrapping paper does she need?&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/wrapping-a-rectangular-box.png\" alt=\"Wrapping a rectangular box\" class=\"wp-image-34208\" title=\"Wrapping a rectangular box\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/wrapping-a-rectangular-box.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/wrapping-a-rectangular-box-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Rectangular box simply means rectangular prism or cuboid. To wrap a rectangular box, Jasmine needs to cover the entire surface of the box.<\/p>\n\n\n\n<p>So, we need to find the TSA.<\/p>\n\n\n\n<p>Here l = 20 m, w = 10 m and h = 7 m<\/p>\n\n\n\n<p>TSA = 2(lw + wh + hl)<\/p>\n\n\n\n<p>TSA&nbsp; = 2 (20 \u2715 10 + 10 \u2715 7 + 20 \u2715 7)&nbsp;<\/p>\n\n\n\n<p>TSA = 2(200 + 70 + 140)&nbsp;<\/p>\n\n\n\n<p>TSA = 2 \u2715 410&nbsp;<\/p>\n\n\n\n<p>TSA = 820 square inches<\/p>\n\n\n\n<p>&nbsp;So, Jasmine needs 820 square inches of wrapping paper.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-facts-about-surface-area-of-rectangular-prism\">Facts about Surface Area of Rectangular Prism<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>If all the edges of a rectangular prism are equal, it becomes a cube and the total surface area = 6 \u2715 area of each face.<\/li>\n\n\n\n<li>Changing the dimensions of a rectangular prism will affect its surface area. Increasing any of the dimensions will result in an increase in surface area, while decreasing the dimensions will lead to a decrease in surface area.<\/li>\n\n\n\n<li>Other common names for a rectangular prism are rectangular box, cuboid, rectangular parallelepiped, rectangular solid.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-solved-examples-on-surface-area-of-rectangular-prism\">Solved Examples on Surface Area of Rectangular Prism<\/h2>\n\n\n\n<p><strong>1. What is the lateral surface area of a rectangular prism with length 10 m, breadth 8 m and height 2 m?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>l = 10 m, w = 8 m, h = 2 m<\/p>\n\n\n\n<p>Lateral Surface Area = 2h(l + w)&nbsp;<\/p>\n\n\n\n<p>Lateral Surface Area = 2 \u2715 2 (10 + 8)<\/p>\n\n\n\n<p>Lateral Surface Area = 4 \u2715 18\u00a0<\/p>\n\n\n\n<p>Lateral Surface Area&nbsp; = 72 square meter<\/p>\n\n\n\n<p><strong>2. What is the total surface area of a rectangular prism with length 42 inches, breadth 30 inches and height 15 inches?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>l = 42 in, b = 30 in, h = 15 in<\/p>\n\n\n\n<p>Total Surface Area = 2(lb + bh + hl)&nbsp;<\/p>\n\n\n\n<p>Total Surface Area = 2(42 \u2715 30 + 30 \u2715 15 + 15 \u2715 42)\u00a0<\/p>\n\n\n\n<p>Total Surface Area = 2(1260 + 450 + 630)&nbsp;<\/p>\n\n\n\n<p>Total Surface Area = 2 \u2715 2340\u00a0<\/p>\n\n\n\n<p>Total Surface Area = 4680 square inches.<\/p>\n\n\n\n<p><strong>3. A fish tank has the shape of a rectangular prism with length (l) = 8 in, Breadth (b) = 5 in and Height (h) = 5 in. What will be the total surface area of the fish tank?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>l = 8 in, b = 5 in, h = 5 in<\/p>\n\n\n\n<p>T.S.A = 2(8 \u2715 5 + 5 \u2715 5 + 5 \u2715 8)\u00a0<\/p>\n\n\n\n<p>T.S.A = 2(40 + 25 + 40)&nbsp;<\/p>\n\n\n\n<p>T.S.A = 2 \u2715 105\u00a0<\/p>\n\n\n\n<p>T.S.A = 210 square inches<\/p>\n\n\n\n<p><strong>4.<\/strong> <strong>Emily built a rectangular box with an open top. The box is 12 inches long, 5 inches wide, and 9 inches high. How much cardboard should she buy?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"323\" height=\"129\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/rectangular-box-with-open-top.png\" alt=\"Rectangular box with open top\" class=\"wp-image-34209\" title=\"Rectangular box with open top\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/rectangular-box-with-open-top.png 323w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/rectangular-box-with-open-top-300x120.png 300w\" sizes=\"auto, (max-width: 323px) 100vw, 323px\" \/><\/figure>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>The box has an open top. So, we will not consider the area of the top face.<\/p>\n\n\n\n<p>l = 12 inches, b = 5 inches, h = 9 inches<\/p>\n\n\n\n<p>Surface Area = lw + 2hl + 2hw&nbsp;<\/p>\n\n\n\n<p>Surface Area = lw + 2h(l + w)<\/p>\n\n\n\n<p>Surface Area = (12 \u2715 5) + 2 \u2715 9 \u2715 (12 + 5)\u00a0<\/p>\n\n\n\n<p>Surface Area = 60 + 306&nbsp;<\/p>\n\n\n\n<p>Surface Area = 366 square inches<\/p>\n\n\n\n<p><strong>5. <\/strong><strong>The total surface area of a rectangular prism is 96 <\/strong>ft2<strong> with a base area of 12 <\/strong>ft2<strong> and the perimeter of the base being 18 ft. Determine its height of the rectangular prism.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>Base Area = Top Area = lb = 12 ft<sup>2<\/sup><\/p>\n\n\n\n<p>Perimeter = 2(l + b) = 18 ft<\/p>\n\n\n\n<p>T.S.A = 96 ft<sup>2<\/sup><\/p>\n\n\n\n<p>2lb + 2h(l + b) = 96<\/p>\n\n\n\n<p>2 \u2715 12 + 18 \u2715 h = 96<\/p>\n\n\n\n<p>24 + 18h = 96<\/p>\n\n\n\n<p>18 h = 72<\/p>\n\n\n\n<p>h = 4 ft<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-practice-problems-on-surface-area-of-rectangular-prism\">Practice Problems on Surface Area of Rectangular Prism<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Surface Area of Rectangular Prism - Formula, Facts, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the formula for surface area of a rectangular prism?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">TSA = 2lw + 2lh<\/div><div class=\"spq_answer_block\" data-value=\"1\">TSA = lwh<\/div><div class=\"spq_answer_block\" data-value=\"2\">TSA = lw<\/div><div class=\"spq_answer_block\" data-value=\"3\">TSA = 2lw + 2wh + 2lh<\/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: TSA = 2lw + 2wh + 2lh<br\/>T.S.A = 2lw + 2wh + 2lh<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">A rectangular prism has a length of 5 units, width of 3 units, and height of 4 units. What is its surface area?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">40 square units<\/div><div class=\"spq_answer_block\" data-value=\"1\">94 square units<\/div><div class=\"spq_answer_block\" data-value=\"2\">60 square units<\/div><div class=\"spq_answer_block\" data-value=\"3\">49 square units<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 94 square units<br\/>TSA = 2(lw + wh + lh)<br>\r\nTSA = 2(5 \u2715 3 + 3 \u2715 4 + 4 \u2715 5)<br>\r\nTSA = 2(15 + 12 + 20)<br>\r\nTSA = 2 \u2715 47<br>\r\nTSA = 94 square units<\/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\">If the length, width, and height of a rectangular prism is doubled, how does the total surface area change?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">It doubles<\/div><div class=\"spq_answer_block\" data-value=\"1\">It halves<\/div><div class=\"spq_answer_block\" data-value=\"2\">It remains the same<\/div><div class=\"spq_answer_block\" data-value=\"3\">It quadruples<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: It quadruples<br\/>Original TSA = 2(lw + wh + lh)<br>\r\nLength, width, and height is doubled.<br>\r\nWidth and height are halved<br>\r\nNew TSA = 2(2l \u2715 2w + 2w \u2715 2h + 2l \u2715 2h)<br>\r\nNew TSA = 2 \u2715 4(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 2(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 Old TSA<br>\r\nThus, the TSA quadruples.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The dimensions of a rectangular box is 15 ft \u2715 9 ft \u2715 12 ft. Find the cost of white washing the faces at the rate of $\\$12$ per square feet.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\$5,076$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\$8,888.5$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\$5,076.5$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\$8,899.5$<\/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: $\\$5,076$<br\/>l = 15 ft , b = 9 ft, h = 12 ft<br>\r\nTSA = 2(lb + lh + bh) = 2(135 + 180 + 108) = 423 square feet<br>\r\nCost of white washing = 423 \u2715 12 = $5,076<\/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 Rectangular Prism - Formula, Facts, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Surface Area of Rectangular Prism\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the formula for surface area of a rectangular prism?\",\n                    \"text\": \"What is the formula for surface area of a rectangular prism?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"T.S.A = 2lw + 2wh + 2lh\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"TSA = 2lw + 2lh\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"T.S.A = 2lw + 2wh + 2lh\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"TSA = lwh\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"T.S.A = 2lw + 2wh + 2lh\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"TSA = lw\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"T.S.A = 2lw + 2wh + 2lh\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"TSA = 2lw + 2wh + 2lh\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"T.S.A = 2lw + 2wh + 2lh\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"T.S.A = 2lw + 2wh + 2lh\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A rectangular prism has a length of 5 units, width of 3 units, and height of 4 units. What is its surface area?\",\n                    \"text\": \"A rectangular prism has a length of 5 units, width of 3 units, and height of 4 units. What is its surface area?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"TSA = 2(lw + wh + lh)<br>\r\nTSA = 2(5 \u2715 3 + 3 \u2715 4 + 4 \u2715 5)<br>\r\nTSA = 2(15 + 12 + 20)<br>\r\nTSA = 2 \u2715 47<br>\r\nTSA = 94 square units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"40 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"TSA = 2(lw + wh + lh)<br>\r\nTSA = 2(5 \u2715 3 + 3 \u2715 4 + 4 \u2715 5)<br>\r\nTSA = 2(15 + 12 + 20)<br>\r\nTSA = 2 \u2715 47<br>\r\nTSA = 94 square units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"60 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"TSA = 2(lw + wh + lh)<br>\r\nTSA = 2(5 \u2715 3 + 3 \u2715 4 + 4 \u2715 5)<br>\r\nTSA = 2(15 + 12 + 20)<br>\r\nTSA = 2 \u2715 47<br>\r\nTSA = 94 square units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"49 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"TSA = 2(lw + wh + lh)<br>\r\nTSA = 2(5 \u2715 3 + 3 \u2715 4 + 4 \u2715 5)<br>\r\nTSA = 2(15 + 12 + 20)<br>\r\nTSA = 2 \u2715 47<br>\r\nTSA = 94 square units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"94 square units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"TSA = 2(lw + wh + lh)<br>\r\nTSA = 2(5 \u2715 3 + 3 \u2715 4 + 4 \u2715 5)<br>\r\nTSA = 2(15 + 12 + 20)<br>\r\nTSA = 2 \u2715 47<br>\r\nTSA = 94 square units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"TSA = 2(lw + wh + lh)<br>\r\nTSA = 2(5 \u2715 3 + 3 \u2715 4 + 4 \u2715 5)<br>\r\nTSA = 2(15 + 12 + 20)<br>\r\nTSA = 2 \u2715 47<br>\r\nTSA = 94 square units\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the length, width, and height of a rectangular prism is doubled, how does the total surface area change?\",\n                    \"text\": \"If the length, width, and height of a rectangular prism is doubled, how does the total surface area change?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Original TSA = 2(lw + wh + lh)<br>\r\nLength, width, and height is doubled.<br>\r\nWidth and height are halved<br>\r\nNew TSA = 2(2l \u2715 2w + 2w \u2715 2h + 2l \u2715 2h)<br>\r\nNew TSA = 2 \u2715 4(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 2(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 Old TSA<br>\r\nThus, the TSA quadruples.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"It doubles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Original TSA = 2(lw + wh + lh)<br>\r\nLength, width, and height is doubled.<br>\r\nWidth and height are halved<br>\r\nNew TSA = 2(2l \u2715 2w + 2w \u2715 2h + 2l \u2715 2h)<br>\r\nNew TSA = 2 \u2715 4(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 2(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 Old TSA<br>\r\nThus, the TSA quadruples.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"It halves\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Original TSA = 2(lw + wh + lh)<br>\r\nLength, width, and height is doubled.<br>\r\nWidth and height are halved<br>\r\nNew TSA = 2(2l \u2715 2w + 2w \u2715 2h + 2l \u2715 2h)<br>\r\nNew TSA = 2 \u2715 4(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 2(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 Old TSA<br>\r\nThus, the TSA quadruples.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"It remains the same\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Original TSA = 2(lw + wh + lh)<br>\r\nLength, width, and height is doubled.<br>\r\nWidth and height are halved<br>\r\nNew TSA = 2(2l \u2715 2w + 2w \u2715 2h + 2l \u2715 2h)<br>\r\nNew TSA = 2 \u2715 4(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 2(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 Old TSA<br>\r\nThus, the TSA quadruples.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"It quadruples\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Original TSA = 2(lw + wh + lh)<br>\r\nLength, width, and height is doubled.<br>\r\nWidth and height are halved<br>\r\nNew TSA = 2(2l \u2715 2w + 2w \u2715 2h + 2l \u2715 2h)<br>\r\nNew TSA = 2 \u2715 4(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 2(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 Old TSA<br>\r\nThus, the TSA quadruples.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Original TSA = 2(lw + wh + lh)<br>\r\nLength, width, and height is doubled.<br>\r\nWidth and height are halved<br>\r\nNew TSA = 2(2l \u2715 2w + 2w \u2715 2h + 2l \u2715 2h)<br>\r\nNew TSA = 2 \u2715 4(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 2(lw + wh + lh)<br>\r\nNew TSA = 4 \u2715 Old TSA<br>\r\nThus, the TSA quadruples.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The dimensions of a rectangular box is 15 ft \u2715 9 ft \u2715 12 ft. Find the cost of white washing the faces at the rate of $$\\\\$$12$$ per square feet.\",\n                    \"text\": \"The dimensions of a rectangular box is 15 ft \u2715 9 ft \u2715 12 ft. Find the cost of white washing the faces at the rate of $$\\\\$$12$$ per square feet.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"l = 15 ft , b = 9 ft, h = 12 ft<br>\r\nTSA = 2(lb + lh + bh) = 2(135 + 180 + 108) = 423 square feet<br>\r\nCost of white washing = 423 \u2715 12 = $$5,076\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\$$8,888.5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"l = 15 ft , b = 9 ft, h = 12 ft<br>\r\nTSA = 2(lb + lh + bh) = 2(135 + 180 + 108) = 423 square feet<br>\r\nCost of white washing = 423 \u2715 12 = $$5,076\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\$$5,076.5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"l = 15 ft , b = 9 ft, h = 12 ft<br>\r\nTSA = 2(lb + lh + bh) = 2(135 + 180 + 108) = 423 square feet<br>\r\nCost of white washing = 423 \u2715 12 = $$5,076\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\$$8,899.5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"l = 15 ft , b = 9 ft, h = 12 ft<br>\r\nTSA = 2(lb + lh + bh) = 2(135 + 180 + 108) = 423 square feet<br>\r\nCost of white washing = 423 \u2715 12 = $$5,076\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\$$5,076$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"l = 15 ft , b = 9 ft, h = 12 ft<br>\r\nTSA = 2(lb + lh + bh) = 2(135 + 180 + 108) = 423 square feet<br>\r\nCost of white washing = 423 \u2715 12 = $$5,076\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"l = 15 ft , b = 9 ft, h = 12 ft<br>\r\nTSA = 2(lb + lh + bh) = 2(135 + 180 + 108) = 423 square feet<br>\r\nCost of white washing = 423 \u2715 12 = $$5,076\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-frequently-asked-questions-on-the-surface-area-of-rectangular-prism\">Frequently Asked Questions on the Surface Area of Rectangular Prism?<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-e7ea703b-edd9-4731-bb0f-8c87c76e0894\" 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-e7ea703b-edd9-4731-bb0f-8c87c76e0894\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e7ea703b-edd9-4731-bb0f-8c87c76e0894\"><strong>What is the volume of Rectangular 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-0-e7ea703b-edd9-4731-bb0f-8c87c76e0894\">\n\n<p>The total space occupied by a rectangular prism is measured by its volume. The volume of a rectangular prism is calculated by multiplying its length, width, and height. The formula for the volume of a rectangular prism is V = length \u00d7 width \u00d7 height.<\/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-e7ea703b-edd9-4731-bb0f-8c87c76e0894\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e7ea703b-edd9-4731-bb0f-8c87c76e0894\"><strong>What is the difference between the surface area of the rectangular prism and volume of the rectangular 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-e7ea703b-edd9-4731-bb0f-8c87c76e0894\">\n\n<p>Surface area represents the total area of the outer faces, volume measures the space enclosed within the prism. Surface area of the rectangular prism is measured in square units. Volume of the rectangular prism is measured in cubic units.<\/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-e7ea703b-edd9-4731-bb0f-8c87c76e0894\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e7ea703b-edd9-4731-bb0f-8c87c76e0894\"><strong>What will be the name of the rectangular prism if all the sides are equal?<\/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-e7ea703b-edd9-4731-bb0f-8c87c76e0894\">\n\n<p>If all the sides of the rectangular prism are equal, then it will be called a cube.<\/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-e7ea703b-edd9-4731-bb0f-8c87c76e0894\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e7ea703b-edd9-4731-bb0f-8c87c76e0894\"><strong>What is the difference between rectangular prism and square 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-3-e7ea703b-edd9-4731-bb0f-8c87c76e0894\">\n\n<p>A rectangular prism is a 3-dimensional solid shape that has 6 faces with its base as rectangles. On the other hand, square prism is a &nbsp;3-dimensional solid shape that has 6 faces with its base as squares.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-e7ea703b-edd9-4731-bb0f-8c87c76e0894\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e7ea703b-edd9-4731-bb0f-8c87c76e0894\"><strong>What is the difference between a rectangular prism and a rectangular 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-4-e7ea703b-edd9-4731-bb0f-8c87c76e0894\">\n\n<p>A rectangular prism is a 3-dimensional solid shape that has 6 faces with its base as rectangles. On the other hand, a rectangular pyramid is a 3-dimensional solid shape with a rectangle as base and faces as triangles.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Surface Area of a Rectangular Prism? The total surface area of a rectangular prism (cuboid) is the total area covered by the surfaces (lateral and base) of a rectangular prism. A rectangular prism consists of 6 faces, each of which are rectangles. Its bases are congruent and parallel to each other. A &#8230; <a title=\"Surface Area of Rectangular Prism &#8211; Formula, Facts, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/surface-area-of-rectangular-prism\" aria-label=\"More on Surface Area of Rectangular Prism &#8211; Formula, Facts, 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-34199","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\/34199","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=34199"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34199\/revisions"}],"predecessor-version":[{"id":34213,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34199\/revisions\/34213"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=34199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=34199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=34199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}