{"id":247419,"date":"2025-07-07T17:32:12","date_gmt":"2025-07-07T17:32:12","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=247419"},"modified":"2025-07-07T17:32:14","modified_gmt":"2025-07-07T17:32:14","slug":"find-the-surface-area-of-a-square-pyramid-with-side-length-5-mi-and-slant-height-4-mi-5-mi-5-mi","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/07\/find-the-surface-area-of-a-square-pyramid-with-side-length-5-mi-and-slant-height-4-mi-5-mi-5-mi\/","title":{"rendered":"‘Find the surface area of a square pyramid with side length 5 mi and slant height = 4 mi. 5 mi 5 mI’"},"content":{"rendered":"\n

‘Find the surface area of a square pyramid with side length 5 mi and slant height = 4 mi. 5 mi 5 mI’<\/p>\n\n\n\n

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

To find the surface area of a square pyramid, we need to calculate the area of both the base and the triangular faces (lateral surface area).<\/p>\n\n\n\n

Formula for the Surface Area of a Square Pyramid:<\/h3>\n\n\n\n

Surface Area=Base Area+Lateral Surface Area\\text{Surface Area} = \\text{Base Area} + \\text{Lateral Surface Area}Surface Area=Base Area+Lateral Surface Area<\/p>\n\n\n\n

    \n
  1. Base Area<\/strong>:
    Since the base of the pyramid is a square, the area of the base is given by: Base\u00a0Area=side\u00a0length2\\text{Base Area} = \\text{side length}^2Base\u00a0Area=side\u00a0length2 Given that the side length is 5 miles, we substitute: Base\u00a0Area=52=25\u2009mi2\\text{Base Area} = 5^2 = 25 \\, \\text{mi}^2Base\u00a0Area=52=25mi2<\/li>\n\n\n\n
  2. Lateral Surface Area<\/strong>:
    The lateral surface area consists of 4 triangular faces. The area of one triangle is: Area\u00a0of\u00a0one\u00a0triangle=12\u00d7base\u00a0of\u00a0triangle\u00d7slant\u00a0height\\text{Area of one triangle} = \\frac{1}{2} \\times \\text{base of triangle} \\times \\text{slant height}Area\u00a0of\u00a0one\u00a0triangle=21\u200b\u00d7base\u00a0of\u00a0triangle\u00d7slant\u00a0height The base of each triangle is the same as the side length of the square (5 miles), and the slant height is 4 miles. Therefore: Area\u00a0of\u00a0one\u00a0triangle=12\u00d75\u00d74=10\u2009mi2\\text{Area of one triangle} = \\frac{1}{2} \\times 5 \\times 4 = 10 \\, \\text{mi}^2Area\u00a0of\u00a0one\u00a0triangle=21\u200b\u00d75\u00d74=10mi2 Since there are 4 triangular faces, the total lateral surface area is: Lateral\u00a0Surface\u00a0Area=4\u00d710=40\u2009mi2\\text{Lateral Surface Area} = 4 \\times 10 = 40 \\, \\text{mi}^2Lateral\u00a0Surface\u00a0Area=4\u00d710=40mi2<\/li>\n\n\n\n
  3. Total Surface Area<\/strong>:
    Finally, the total surface area is the sum of the base area and the lateral surface area: Surface\u00a0Area=25+40=65\u2009mi2\\text{Surface Area} = 25 + 40 = 65 \\, \\text{mi}^2Surface\u00a0Area=25+40=65mi2<\/li>\n<\/ol>\n\n\n\n

    Final Answer:<\/h3>\n\n\n\n

    The surface area of the square pyramid is 65 square miles<\/strong>.<\/p>\n\n\n\n

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

    ‘Find the surface area of a square pyramid with side length 5 mi and slant height = 4 mi. 5 mi 5 mI’ The Correct Answer and Explanation is: To find the surface area of a square pyramid, we need to calculate the area of both the base and the triangular faces (lateral 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-247419","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/247419","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=247419"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/247419\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=247419"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=247419"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=247419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}