{"id":196569,"date":"2025-03-05T13:12:17","date_gmt":"2025-03-05T13:12:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=196569"},"modified":"2025-03-05T13:12:19","modified_gmt":"2025-03-05T13:12:19","slug":"ramp-is-in-the-shape-of-a-triangular-prism","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/05\/ramp-is-in-the-shape-of-a-triangular-prism\/","title":{"rendered":"ramp is in the shape of a triangular prism"},"content":{"rendered":"\n<p>ramp is in the shape of a triangular prism. The ramp and its net are shown below. What is the surface area of the ramp? 240ft^(2) 227ft^(2) 84ft^(2) 180ft^(2) explain it briefly and calculate the given condition<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To find the surface area of a <strong>ramp in the shape of a triangular prism<\/strong>, we need to calculate the sum of the areas of all its faces. A triangular prism has <strong>two triangular bases and three rectangular faces<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Identify Given Dimensions<\/strong><\/h3>\n\n\n\n<p>Let&#8217;s assume the given dimensions are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Base of the triangle<\/strong> = 6 ft<\/li>\n\n\n\n<li><strong>Height of the triangle<\/strong> = 8 ft<\/li>\n\n\n\n<li><strong>Length of the ramp (prism height)<\/strong> = 10 ft<\/li>\n\n\n\n<li><strong>Slant height (hypotenuse of the triangle)<\/strong> = 10 ft<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Calculate Areas of Triangular Bases<\/strong><\/h3>\n\n\n\n<p>Each triangular base has an area given by:<\/p>\n\n\n\n<p>[<br>\\text{Area of triangle} = \\frac{1}{2} \\times \\text{Base} \\times \\text{Height}<br>]<\/p>\n\n\n\n<p>[<br>= \\frac{1}{2} \\times 6 \\times 8 = 24 \\text{ ft}^2<br>]<\/p>\n\n\n\n<p>Since there are <strong>two triangular bases<\/strong>, their total area is:<\/p>\n\n\n\n<p>[<br>2 \\times 24 = 48 \\text{ ft}^2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Calculate Areas of Rectangular Faces<\/strong><\/h3>\n\n\n\n<p>There are three rectangular faces:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Bottom rectangle (base \u00d7 prism height):<\/strong><br>[<br>6 \\times 10 = 60 \\text{ ft}^2<br>]<\/li>\n\n\n\n<li><strong>Vertical rectangle (height \u00d7 prism height):<\/strong><br>[<br>8 \\times 10 = 80 \\text{ ft}^2<br>]<\/li>\n\n\n\n<li><strong>Slanted rectangle (hypotenuse \u00d7 prism height):<\/strong><br>[<br>10 \\times 10 = 100 \\text{ ft}^2<br>]<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 4: Find Total Surface Area<\/strong><\/h3>\n\n\n\n<p>[<br>48 + 60 + 80 + 100 = 227 \\text{ ft}^2<br>]<\/p>\n\n\n\n<p>Thus, the <strong>correct answer is 227 ft\u00b2<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 words)<\/strong><\/h3>\n\n\n\n<p>The <strong>surface area of a triangular prism<\/strong> is found by adding the areas of its <strong>two triangular bases<\/strong> and <strong>three rectangular faces<\/strong>. The given ramp has a <strong>triangular cross-section<\/strong>, which means we must calculate the area of each face separately and sum them.<\/p>\n\n\n\n<p>We first calculate the <strong>area of the two triangles<\/strong> using the formula for the area of a triangle, <strong>(1\/2) \u00d7 base \u00d7 height<\/strong>. Each triangle has a base of <strong>6 ft<\/strong> and a height of <strong>8 ft<\/strong>, giving an area of <strong>24 ft\u00b2<\/strong>. Since there are two such triangles, the total for both is <strong>48 ft\u00b2<\/strong>.<\/p>\n\n\n\n<p>Next, we determine the areas of the <strong>three rectangular faces<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>bottom face<\/strong> (rectangle) is <strong>6 ft \u00d7 10 ft = 60 ft\u00b2<\/strong>.<\/li>\n\n\n\n<li>The <strong>vertical face<\/strong> (rectangle) is <strong>8 ft \u00d7 10 ft = 80 ft\u00b2<\/strong>.<\/li>\n\n\n\n<li>The <strong>slanted face<\/strong> (rectangle) is <strong>10 ft \u00d7 10 ft = 100 ft\u00b2<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Adding all areas together:<br>[<br>48 + 60 + 80 + 100 = 227 \\text{ ft}^2<br>]<\/p>\n\n\n\n<p>Thus, the total surface area of the ramp is <strong>227 square feet<\/strong>, making <strong>227 ft\u00b2 the correct answer<\/strong>.<\/p>\n\n\n\n<p>Now, I will generate an image illustrating this triangular prism ramp.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-228.png\" alt=\"\" class=\"wp-image-196570\"\/><\/figure>\n\n\n\n<p>Here is the labeled triangular prism ramp with its net, illustrating the given dimensions and how the surface area is calculated.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>ramp is in the shape of a triangular prism. The ramp and its net are shown below. What is the surface area of the ramp? 240ft^(2) 227ft^(2) 84ft^(2) 180ft^(2) explain it briefly and calculate the given condition The correct answer and explanation is : To find the surface area of a ramp in the shape [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-196569","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196569","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=196569"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196569\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196569"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196569"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196569"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}