{"id":258801,"date":"2025-07-18T12:47:43","date_gmt":"2025-07-18T12:47:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=258801"},"modified":"2025-07-18T13:39:31","modified_gmt":"2025-07-18T13:39:31","slug":"the-net-of-a-triangular-prism-whose-bases-are-equilateral-triangles-is-shown-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/18\/the-net-of-a-triangular-prism-whose-bases-are-equilateral-triangles-is-shown-below\/","title":{"rendered":"The net of a triangular prism whose bases are equilateral triangles is shown below."},"content":{"rendered":"\n

The net of a triangular prism whose bases are equilateral triangles is shown below. What is the total surface area of the triangular prism?<\/p>\n\n\n\n

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

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

To find the total surface area of a triangular prism with equilateral triangle bases, we can break the problem into simpler steps by calculating the areas of the faces that make up the surface area. A triangular prism consists of:<\/p>\n\n\n\n

    \n
  1. Two equilateral triangle bases<\/strong>:
    The area of an equilateral triangle with side length sss is given by the formula: A=34s2A = \\frac{\\sqrt{3}}{4} s^2A=43\u200b\u200bs2 So, the area of each base is 34s2\\frac{\\sqrt{3}}{4} s^243\u200b\u200bs2. Since there are two such triangles (one on the top and one on the bottom), the total area for the bases is: Abases=2\u00d734s2=32s2A_{\\text{bases}} = 2 \\times \\frac{\\sqrt{3}}{4} s^2 = \\frac{\\sqrt{3}}{2} s^2Abases\u200b=2\u00d743\u200b\u200bs2=23\u200b\u200bs2<\/li>\n\n\n\n
  2. Three rectangular lateral faces<\/strong>:
    The lateral faces are rectangles that connect the corresponding sides of the two equilateral triangles. Each rectangle has a width equal to the side length sss of the triangles, and the height is the length of the prism, denoted as hhh. The area of one rectangular face is: Arect=s\u00d7hA_{\\text{rect}} = s \\times hArect\u200b=s\u00d7h Since there are three rectangular faces, the total area for the lateral faces is: Alateral=3\u00d7(s\u00d7h)=3shA_{\\text{lateral}} = 3 \\times (s \\times h) = 3shAlateral\u200b=3\u00d7(s\u00d7h)=3sh<\/li>\n\n\n\n
  3. Total surface area<\/strong>:
    Finally, to find the total surface area, we add the area of the two triangular bases and the area of the three rectangular lateral faces: Atotal=Abases+Alateral=32s2+3shA_{\\text{total}} = A_{\\text{bases}} + A_{\\text{lateral}} = \\frac{\\sqrt{3}}{2} s^2 + 3shAtotal\u200b=Abases\u200b+Alateral\u200b=23\u200b\u200bs2+3sh<\/li>\n<\/ol>\n\n\n\n

    Thus, the total surface area of the triangular prism is:Atotal=32s2+3shA_{\\text{total}} = \\frac{\\sqrt{3}}{2} s^2 + 3shAtotal\u200b=23\u200b\u200bs2+3sh<\/p>\n\n\n\n

    This formula gives the surface area of a triangular prism with equilateral triangle bases, where sss is the side length of the equilateral triangle and hhh is the height (or length) of the prism.<\/p>\n\n\n\n

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

    The net of a triangular prism whose bases are equilateral triangles is shown below. What is the total surface area of the triangular prism? The Correct Answer and Explanation is: To find the total surface area of a triangular prism with equilateral triangle bases, we can break the problem into simpler steps by calculating the […]<\/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-258801","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258801","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=258801"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258801\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258801"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258801"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258801"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}