Given an equilateral triangular prism with base edge 13 cm and height of 3 cm. Find the measure of the lateral area, surface area, and volume. Round to the nearest tenth. Given an equilateral triangular prism with base edge 13 cm and height of 3 cm. Find the measure of the lateral area, surface area, and volume. Round to the nearest tenth.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve for the lateral area, surface area, and volume of the given equilateral triangular prism, we need to use specific formulas. The prism has a base edge of 13 cm and a height of 3 cm.<\/p>\n\n\n\n The lateral area of a prism is the area of the sides of the prism, excluding the bases. For a triangular prism, the lateral area is given by:<\/p>\n\n\n\n [ The perimeter (P) of an equilateral triangle with base edge (s) is:<\/p>\n\n\n\n [ Now, using the height (h = 3 \\, \\text{cm}), the lateral area is:<\/p>\n\n\n\n [ The surface area of the prism is the sum of the lateral area and the area of the two triangular bases.<\/p>\n\n\n\n The area (A_{\\text{triangle}}) of an equilateral triangle is given by:<\/p>\n\n\n\n [ Substitute (s = 13):<\/p>\n\n\n\n [ The surface area of the prism is:<\/p>\n\n\n\n [ The volume of the prism is the area of the triangular base multiplied by the height of the prism:<\/p>\n\n\n\n [ Given an equilateral triangular prism with base edge 13 cm and height of 3 cm. Find the measure of the lateral area, surface area, and volume. Round to the nearest tenth. Given an equilateral triangular prism with base edge 13 cm and height of 3 cm. Find the measure of the lateral area, surface 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-192368","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192368","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=192368"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192368\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=192368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=192368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=192368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}1. Lateral Area<\/strong>:<\/h3>\n\n\n\n
\\text{Lateral Area} = \\text{Perimeter of the base} \\times \\text{Height of the prism}
]<\/p>\n\n\n\nStep 1: Find the perimeter of the equilateral triangle base.<\/h4>\n\n\n\n
P = 3 \\times s = 3 \\times 13 = 39 \\, \\text{cm}
]<\/p>\n\n\n\nStep 2: Calculate the lateral area.<\/h4>\n\n\n\n
\\text{Lateral Area} = 39 \\times 3 = 117 \\, \\text{cm}^2
]<\/p>\n\n\n\n2. Surface Area<\/strong>:<\/h3>\n\n\n\n
Step 1: Find the area of the triangular base.<\/h4>\n\n\n\n
A_{\\text{triangle}} = \\frac{\\sqrt{3}}{4} \\times s^2
]<\/p>\n\n\n\n
A_{\\text{triangle}} = \\frac{\\sqrt{3}}{4} \\times 13^2 = \\frac{\\sqrt{3}}{4} \\times 169 \\approx 73.6 \\, \\text{cm}^2
]<\/p>\n\n\n\nStep 2: Calculate the surface area.<\/h4>\n\n\n\n
\\text{Surface Area} = \\text{Lateral Area} + 2 \\times A_{\\text{triangle}} = 117 + 2 \\times 73.6 = 117 + 147.2 = 264.2 \\, \\text{cm}^2
]<\/p>\n\n\n\n3. Volume<\/strong>:<\/h3>\n\n\n\n
\\text{Volume} = A_{\\text{triangle}} \\times h = 73.6 \\times 3 = 220.8 \\, \\text{cm}^3
]<\/p>\n\n\n\nFinal Answers:<\/h3>\n\n\n\n
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