{"id":258795,"date":"2025-07-18T12:45:35","date_gmt":"2025-07-18T12:45:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=258795"},"modified":"2025-07-18T12:45:37","modified_gmt":"2025-07-18T12:45:37","slug":"the-base-of-the-triangular-prism","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/18\/the-base-of-the-triangular-prism\/","title":{"rendered":"The base of the triangular prism"},"content":{"rendered":"\n<p>The base of the triangular prism is an equilateral triangle with side length 2.8 cm. 2.8 cm 1.4 cm 1.2 cm 4.8 cm<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-524.png\" alt=\"\" class=\"wp-image-258796\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Based on the provided image and geometric principles, the correct answer is the total volume of the composite solid.<\/p>\n\n\n\n<p><strong>Correct Answer: 22.90 cm\u00b3<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>The image displays a composite 3D shape, which consists of a rectangular prism at the bottom and a triangular prism on top. To find the total volume of this object, we must calculate the volume of each individual shape and then add them together.<\/p>\n\n\n\n<p>First, we calculate the volume of the rectangular prism. The formula for the volume of a rectangular prism is Volume = Length \u00d7 Width \u00d7 Height. According to the diagram, the dimensions are a length of 4.8 cm, a width of 2.8 cm, and a height of 1.4 cm.<br>Volume of rectangular prism = 4.8 cm \u00d7 2.8 cm \u00d7 1.4 cm = 18.816 cm\u00b3.<\/p>\n\n\n\n<p>Next, we calculate the volume of the triangular prism. The formula for its volume is Volume = Area of the base \u00d7 Height of the prism. The text specifies that the base is an equilateral triangle with a side length of 2.8 cm. The area of an equilateral triangle is found using the formula Area = (s\u00b2\u221a3) \/ 4, where &#8216;s&#8217; is the side length.<br>Area of the triangular base = (2.8\u00b2 \u00d7 \u221a3) \/ 4<br>Area = (7.84 \u00d7 \u221a3) \/ 4 \u2248 3.395 cm\u00b2.<br>The height (or length) of the triangular prism, which is the distance between its two triangular faces, is given as 1.2 cm.<br>Volume of triangular prism = 3.395 cm\u00b2 \u00d7 1.2 cm \u2248 4.074 cm\u00b3.<\/p>\n\n\n\n<p>Finally, to find the total volume of the entire object, we sum the volumes of the two component shapes.<br>Total Volume = Volume of rectangular prism + Volume of triangular prism<br>Total Volume = 18.816 cm\u00b3 + 4.074 cm\u00b3 = 22.89 cm\u00b3.<\/p>\n\n\n\n<p>Rounding the final result to two decimal places gives a total volume of 22.90 cm\u00b3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner9-240.jpeg\" alt=\"\" class=\"wp-image-258797\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The base of the triangular prism is an equilateral triangle with side length 2.8 cm. 2.8 cm 1.4 cm 1.2 cm 4.8 cm The Correct Answer and Explanation is: Based on the provided image and geometric principles, the correct answer is the total volume of the composite solid. Correct Answer: 22.90 cm\u00b3 Explanation The image [&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-258795","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258795","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=258795"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258795\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258795"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258795"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258795"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}