{"id":233378,"date":"2025-06-13T05:43:30","date_gmt":"2025-06-13T05:43:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233378"},"modified":"2025-06-13T05:43:32","modified_gmt":"2025-06-13T05:43:32","slug":"what-is-the-volume-of-the-right-triangular-prism-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/what-is-the-volume-of-the-right-triangular-prism-below\/","title":{"rendered":"What is the volume of the right triangular prism below"},"content":{"rendered":"\n

What is the volume of the right triangular prism below? 9 yd 21 yd 6 yd<\/p>\n\n\n\n

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

To find the volume of a right triangular prism<\/strong>, we use the formula:Volume=Area of the triangular base\u00d7Height (or length) of the prism\\text{Volume} = \\text{Area of the triangular base} \\times \\text{Height (or length) of the prism}Volume=Area of the triangular base\u00d7Height (or length) of the prism<\/p>\n\n\n\n

Step 1: Identify the dimensions<\/h3>\n\n\n\n

From the information provided:<\/p>\n\n\n\n

    \n
  • The triangular base has legs of 9 yd and 6 yd<\/strong>, meaning it is a right triangle<\/strong> with these two sides forming the right angle.<\/li>\n\n\n\n
  • The length or height of the prism (distance between the two triangular bases) is 21 yd<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    Step 2: Find the area of the triangular base<\/h3>\n\n\n\n

    For a right triangle<\/strong>, the area is given by:Area=12\u00d7base\u00d7height\\text{Area} = \\frac{1}{2} \\times \\text{base} \\times \\text{height}Area=21\u200b\u00d7base\u00d7height<\/p>\n\n\n\n

    Here, base = 9 yd and height = 6 yd.Area=12\u00d79\u00d76=12\u00d754=27 square yards\\text{Area} = \\frac{1}{2} \\times 9 \\times 6 = \\frac{1}{2} \\times 54 = 27 \\text{ square yards}Area=21\u200b\u00d79\u00d76=21\u200b\u00d754=27 square yards<\/p>\n\n\n\n

    Step 3: Multiply by the height (length) of the prism<\/h3>\n\n\n\n

    Volume=Area of triangle\u00d7Length of prism=27\u00d721=567 cubic yards\\text{Volume} = \\text{Area of triangle} \\times \\text{Length of prism} = 27 \\times 21 = 567 \\text{ cubic yards}Volume=Area of triangle\u00d7Length of prism=27\u00d721=567 cubic yards<\/p>\n\n\n\n

    \n\n\n\n

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

    The volume of the triangular prism is 567 cubic yards.<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    Textbook-style Explanation (300 words):<\/h3>\n\n\n\n

    The volume of a three-dimensional solid refers to the amount of space it occupies. For prisms, this volume is calculated by multiplying the area of the base by the height (or length) of the prism. In the case of a right triangular prism, the base is a triangle, and the prism extends uniformly along its height.<\/p>\n\n\n\n

    To calculate the volume of a right triangular prism, begin by determining the area of its triangular base. If the triangle is a right triangle<\/strong>, its area can be found using the formula:Area=12\u00d7base\u00d7height\\text{Area} = \\frac{1}{2} \\times \\text{base} \\times \\text{height}Area=21\u200b\u00d7base\u00d7height<\/p>\n\n\n\n

    In this problem, the triangle has legs of 9 yards and 6 yards, which are perpendicular. Substituting into the formula gives:12\u00d79\u00d76=27 square yards\\frac{1}{2} \\times 9 \\times 6 = 27 \\text{ square yards}21\u200b\u00d79\u00d76=27 square yards<\/p>\n\n\n\n

    This value represents the area of one triangular base. The prism extends 21 yards along its length. Therefore, the volume is found by:Volume=27\u00d721=567 cubic yards\\text{Volume} = 27 \\times 21 = 567 \\text{ cubic yards}Volume=27\u00d721=567 cubic yards<\/p>\n\n\n\n

    This means the prism encloses 567 cubic yards of space. It is important to ensure that all dimensions are in the same units before calculating volume, and to correctly apply the area formula for a triangle. This method can be extended to any triangular prism, as long as the correct base and height are identified.<\/p>\n\n\n\n

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

    What is the volume of the right triangular prism below? 9 yd 21 yd 6 yd The Correct Answer and Explanation is: To find the volume of a right triangular prism, we use the formula:Volume=Area of the triangular base\u00d7Height (or length) of the prism\\text{Volume} = \\text{Area of the triangular base} \\times \\text{Height (or length) of the prism}Volume=Area of the triangular base\u00d7Height (or length) of the prism Step 1: Identify the dimensions From 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-233378","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233378","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=233378"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233378\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233378"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233378"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}