{"id":327,"date":"2024-05-11T05:30:58","date_gmt":"2024-05-11T05:30:58","guid":{"rendered":"https:\/\/casestudyhelp.net\/questions\/?p=327"},"modified":"2024-05-11T05:30:58","modified_gmt":"2024-05-11T05:30:58","slug":"rectangular-prism-definition-and-example","status":"publish","type":"post","link":"https:\/\/casestudyhelp.net\/questions\/rectangular-prism-definition-and-example\/","title":{"rendered":"Rectangular Prism: Definition and Example"},"content":{"rendered":"<h2>Rectangular Prism: Definition and Example<\/h2>\n<p style=\"background: white;\"><strong><span style=\"color: black;\">Answer:<\/span><\/strong><\/p>\n<p style=\"background: white;\"><span style=\"font-size: 13.5pt; color: black;\">Rectangular prisms are three-dimensional shapes with six faces. The top, bottom, and lateral faces of a prism are all rectangles, and all pairs of opposing faces of the prism are congruent. Rectangular prism have surface area and volume, just like any other three-dimensional form. The term \u201ccuboid\u201d also applies to rectangular prisms.<\/span><\/p>\n<h3>Rectangular Prism<strong> specifications include:<\/strong><\/h3>\n<ul>\n<li>Have three dimensions: height, width, and depth.<\/li>\n<li>Exhibit parallel, polygonal faces<\/li>\n<li>Take the shape of a hexahedron.<\/li>\n<li>Possess sides that are structured like a parallelogram; this is significant since it sets a rectangular prism apart from a triangular prism.<\/li>\n<li>Consist of 8 vertices and 12 edges.<\/li>\n<\/ul>\n<h3><strong>Characteristics of a Rectangular Prism:<\/strong><\/h3>\n<ul>\n<li>Six rectangular faces, twelve sides, and eight vertices form a rectangular prism.<\/li>\n<li>A rectangular prism has congruent opposite sides on all of them.<\/li>\n<li>There is a rectangular cross-section in a rectangular prism.<\/li>\n<li>A straight line joining two sides defines a 3D shape\u2019s edge.<\/li>\n<li>To make it easier for us to recognize particular edges or faces, you can label the vertices, or corners, of a rectangular prism.<\/li>\n<\/ul>\n<h3><strong>Different Types of Rectangles Prism<\/strong><\/h3>\n<p>Oblique and cuboid are the two types of rectangular prisms. Let\u2019s know about them in brief.<\/p>\n<ul>\n<li><strong>Oblique:<\/strong> The faces of an oblique rectangular prism are not parallel to the bases. To put it another way, this prism\u2019s faces are parallelograms.<\/li>\n<li><strong>Cuboid: <\/strong>A cuboid has equal and parallel opposing faces, and all of its angles are right angles. An alternative name for this three-dimensional structure is a right rectangular prism. It should be noted that not all cuboids are cubes, but cubes are cuboids. Refrigerators and aquariums are two real-world instances of right rectangular prisms\/cuboids.<\/li>\n<\/ul>\n<h3 style=\"background: white;\"><strong><span style=\"color: black;\">Volume and Surface Area<\/span><\/strong><\/h3>\n<p style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size); font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; word-spacing: 0px;\"><span style=\"font-size: 13.5pt; color: black;\">There are three dimensions to the rectangular prism. It indicates that it has a volume and a surface area.<\/span><\/p>\n<p style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size); font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; word-spacing: 0px;\"><span style=\"font-size: 13.5pt; color: black;\">The following formula can be used to determine a rectangular prism\u2019s surface area as all of its sides are rectangles and its opposite faces are equal:<\/span><\/p>\n<p style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size); font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; word-spacing: 0px;\"><b><span style=\"font-size: 13.5pt; color: black;\">Total Surface Area: <\/span><\/b><span style=\"font-size: 13.5pt; color: black;\">2 (width x length) + (length x height) + (width x height)<\/span><\/p>\n<p style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size); font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; word-spacing: 0px;\"><b><span style=\"font-size: 13.5pt; color: black;\">Lateral Surface Area: <\/span><\/b><span style=\"font-size: 13.5pt; color: black;\">2 (length x height) + (width x height)<\/span><\/p>\n<p style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size); font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; word-spacing: 0px;\"><span style=\"font-size: 13.5pt; color: black;\">Multiplying each of the three dimensions gives the volume of a rectangular prism.<\/span><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/casestudyhelp.net\/order-now.php\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1341 size-full\" src=\"https:\/\/casestudyhelp.net\/questions\/wp-content\/uploads\/2024\/05\/Ask-an-expert-QA.webp\" alt=\"Get Assignment Help\" width=\"800\" height=\"180\" \/><\/a><\/p>\n<h3 style=\"background: white;\"><span style=\"color: black;\">Formulas for Rectangular Prisms<\/span><\/h3>\n<p style=\"background: white; margin-block: 1.5rem 0px; max-width: var(--wp--style--global--content-size); font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; word-spacing: 0px;\"><span style=\"font-size: 13.5pt; color: black;\">We will now get the formulas for a rectangular prism\u2019s surface area and volume. Let us assume a rectangular prism with dimensions of length \u2018l\u2019, width \u2018w\u2019, and height \u2018h\u2019 for each of these. Let\u2019s assume that \u2018l\u2019 and \u2018w\u2019 represent the base\u2019s measurements along these lines. The following are the formulas for a rectangular prism\u2019s surface area and volume.<\/span><\/p>\n<p>Volume, V = lwh<\/p>\n<p>Total surface area = 2 (l+wh+hl)<\/p>\n<p>Lateral surface area = 2 (wh+hl)<\/p>\n<h3><strong><u>Solved Examples<\/u><\/strong><\/h3>\n<p><strong><u>Example 1<\/u><\/strong><\/p>\n<p><strong>Ques:<\/strong> Given a right rectangular prism with dimensions of 5 feet by 4 feet for width, 6 feet for height, and 4 feet for length, what is the total area?<\/p>\n<p><strong>Sol: Total surface area = 2 (WL) + (LH) + (WH)<\/strong><\/p>\n<p>2 (45) + (56) + (46)<\/p>\n<p>2 (20) + (30) + (24)<\/p>\n<p>148 ft2<\/p>\n<h3><strong><u>Example 2<\/u><\/strong><\/h3>\n<p><strong>Ques:<\/strong> Find the lateral and total surface area of a rectangular prism with length 16 cm, width 12.5 cm, and height 10 cm.<\/p>\n<p><strong>Sol:<\/strong> Given what is known,<\/p>\n<p>Lateral Surface Area (LSA) is equal to 2(wh + hl), where w = 12.5 cm, h = 10 cm, and l = 16 cm.<\/p>\n<p>Therefore, LSA is equal to 2(12.5 \u00d7 10 + 10 \u00d7 16).<\/p>\n<p>= 570 square centimeters.<\/p>\n<p>The formula for Total Surface Area (TSA) is 2(lw + wh + hl), where l is 16 cm, w is 12.5 cm, and h is 10 cm.<\/p>\n<p>\u2228 TSA = 2(16 \u00d7 12.5 + 12.5 \u00d7 10 + 10 \u00d7 16)<\/p>\n<p>= 970 cm2<\/p>\n<h3><strong><u>Example 3<\/u><\/strong><\/h3>\n<p><strong>Ques:<\/strong> Determine the volume of a rectangular prism using the following measurements: 7 cm for length, 6 cm for width, and 4 cm for height.<\/p>\n<p><strong>Sol:<\/strong> Given,<\/p>\n<p>length, l = 7 cm.<\/p>\n<p>breadth, w = 6 cm<\/p>\n<p>Height: h = 4 cm<\/p>\n<p>According to l.w.h., the volume of a rectangular prism<\/p>\n<p>L x W x H is the cubic unit of V.<\/p>\n<p>Enter the values for l, w, and h in the formula.<\/p>\n<p>V is equivalent to 7 x 6 x 4 cm^.<\/p>\n<p>Consequently, 168 cm\u00b3 is the volume of a rectangular prism.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rectangular Prism: Definition and Example Answer: Rectangular prisms are three-dimensional shapes with six faces. 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