{"id":226694,"date":"2025-06-05T12:57:45","date_gmt":"2025-06-05T12:57:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226694"},"modified":"2025-06-05T12:57:47","modified_gmt":"2025-06-05T12:57:47","slug":"shauns-tent-shown-below-is-a-triangular-prism","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/05\/shauns-tent-shown-below-is-a-triangular-prism\/","title":{"rendered":"Shaun’s tent (shown below) is a triangular prism."},"content":{"rendered":"\n

Shaun’s tent (shown below) is a triangular prism. Find the surface area, including the floor, of his tent: Dimensions: Length: 3 m Width: 3 m Height: 2.6 m The formula to calculate the surface area of a triangular prism is: Surface Area = 2 * (base area) + (lateral area) To find the base area, we need to calculate the area of the triangular base. Since it is an equilateral triangle, we can use the formula: Base Area = (sqrt(3) \/ 4) * (side length)^2 Substituting the values, we get: Base Area = (sqrt(3) \/ 4) * (3 m)^2 To find the lateral area, we need to calculate the area of the three rectangular faces. The formula for the area of a rectangle is: Area = length * width Substituting the values, we get: Lateral Area = 3 m * 2.6 m + 3 m * 2.6 m + 2.6 m * 2.6 m Finally, we can calculate the surface area by substituting the values into the formula: Surface Area = 2 * (Base Area) + (Lateral Area)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s calculate the surface area of Shaun’s tent, which is a triangular prism<\/strong>. The diagram shows a triangular front face with base 3 meters and height 2.6 meters, and the prism has a length (depth) of 5 meters.<\/p>\n\n\n\n

\n\n\n\n

Step 1: Calculate the area of the triangular base<\/strong><\/h3>\n\n\n\n

The area of a triangle is: Base Area=12\u00d7base\u00d7height\\text{Base Area} = \\frac{1}{2} \\times \\text{base} \\times \\text{height}<\/p>\n\n\n\n

Given:<\/p>\n\n\n\n

    \n
  • Base = 3 m<\/li>\n\n\n\n
  • Height = 2.6 m<\/li>\n<\/ul>\n\n\n\n

    Base Area=12\u00d73\u00d72.6=3.9 m2\\text{Base Area} = \\frac{1}{2} \\times 3 \\times 2.6 = 3.9 \\text{ m}^2<\/p>\n\n\n\n

    Since there are two identical triangular faces: Total Area of Triangular Faces=2\u00d73.9=7.8 m2\\text{Total Area of Triangular Faces} = 2 \\times 3.9 = 7.8 \\text{ m}^2<\/p>\n\n\n\n

    \n\n\n\n

    Step 2: Calculate the lateral (rectangular) surface areas<\/strong><\/h3>\n\n\n\n

    There are three rectangles<\/strong> forming the sides:<\/p>\n\n\n\n

      \n
    • Bottom rectangle (floor)<\/strong>: base \u00d7 length = 3 m \u00d7 5 m = 15 m\u00b2<\/li>\n\n\n\n
    • Two slanted sides<\/strong> (each has side length 3 m and length 5 m):<\/li>\n<\/ul>\n\n\n\n

      Each slanted side area=3\u00d75=15 m2\\text{Each slanted side area} = 3 \\times 5 = 15 \\text{ m}^2 Total Lateral Area=15+15+15=45 m2\\text{Total Lateral Area} = 15 + 15 + 15 = 45 \\text{ m}^2<\/p>\n\n\n\n

      \n\n\n\n

      Step 3: Add base areas and lateral area<\/strong><\/h3>\n\n\n\n

      Total Surface Area=7.8+45=52.8 m2\\text{Total Surface Area} = 7.8 + 45 = \\boxed{52.8 \\text{ m}^2}<\/p>\n\n\n\n

      \n\n\n\n

      \u2705 Final Answer: 52.8 m\u00b2<\/strong><\/h3>\n\n\n\n
      \n\n\n\n

      \u270f\ufe0f Explanation <\/strong><\/h3>\n\n\n\n

      To calculate the surface area of Shaun\u2019s tent, we use the formula for the surface area of a triangular prism:
      Surface Area = 2 \u00d7 (Base Area) + Lateral Area.<\/strong><\/p>\n\n\n\n

      The tent\u2019s two triangular ends are identical, forming the bases. From the diagram, each triangle has a base of 3 meters<\/strong> and a height of 2.6 meters<\/strong>. Using the triangle area formula 12\u00d7base\u00d7height\\frac{1}{2} \\times \\text{base} \\times \\text{height}, each triangular face is 3.93.9 square meters. Since there are two of them, the total area from these faces is 2\u00d73.9=7.82 \\times 3.9 = 7.8 m\u00b2.<\/p>\n\n\n\n

      The lateral area comes from the three rectangular sides of the prism:<\/p>\n\n\n\n

        \n
      1. The bottom rectangle (the floor of the tent) has dimensions 3 m by 5 m<\/strong>, so its area is 15 m\u00b2<\/strong>.<\/li>\n\n\n\n
      2. Each slanted side is a rectangle with dimensions 3 m by 5 m<\/strong>, resulting in 15 m\u00b2<\/strong> each.<\/li>\n<\/ol>\n\n\n\n

        Adding these: 15+15+15=4515 + 15 + 15 = 45 m\u00b2.<\/p>\n\n\n\n

        Finally, we sum the triangle faces (7.8 m\u00b2) and the rectangular sides (45 m\u00b2) to get the total surface area: 52.8 m2\\boxed{52.8 \\text{ m}^2}<\/p>\n\n\n\n

        This includes all outer sides and<\/strong> the floor, as required.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Shaun’s tent (shown below) is a triangular prism. Find the surface area, including the floor, of his tent: Dimensions: Length: 3 m Width: 3 m Height: 2.6 m The formula to calculate the surface area of a triangular prism is: Surface Area = 2 * (base area) + (lateral area) To find the base area, […]<\/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-226694","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226694","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=226694"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226694\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226694"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226694"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226694"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}