{"id":30304,"date":"2023-06-09T09:16:02","date_gmt":"2023-06-09T09:16:02","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=30304"},"modified":"2023-11-15T16:48:31","modified_gmt":"2023-11-15T16:48:31","slug":"parallelepiped-definition-formula-volume-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/parallelepiped","title":{"rendered":"Parallelepiped: Definition, Formula, Volume, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-a6a88077-9bac-4f48-93fa-4824138fdc43\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/parallelepiped#0-what-is-a-parallelepiped-in-math>What Is a Parallelepiped in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/parallelepiped#3-difference-between-parallelogram-and-parallelepiped>Difference between Parallelogram and Parallelepiped<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/parallelepiped#5-lateral-surface-area-of-parallelepiped>Lateral Surface Area of Parallelepiped<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/parallelepiped#12-solved-examples-on-parallelepipeds>Solved Examples on Parallelepipeds<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/parallelepiped#13-practice-problems-on-parallelepipeds>Practice Problems on Parallelepipeds<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/parallelepiped#14-frequently-asked-questions-on-parallelepipeds>Frequently Asked Questions on Parallelepipeds<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-a-parallelepiped-in-math\">What Is a Parallelepiped in Math?<\/h2>\n\n\n\n<p><strong>A parallelepiped is a three-dimensional <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/geometric-solid\" target=\"_blank\" rel=\"noopener\" title=\"\"><strong>geometric solid<\/strong><\/a><strong> with six faces such that each face is a parallelogram. It is also called a <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/prism\" target=\"_blank\" rel=\"noopener\" title=\"\"><strong>prism<\/strong><\/a><strong> with a parallelogram base.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"191\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-parallelepiped-its-base-and-height.png\" alt=\"A parallelepiped, its base and height\" class=\"wp-image-35827\" title=\"A parallelepiped, its base and height\"\/><\/figure>\n\n\n\n<p>A parallelepiped is a polyhedron since it is formed by 6 parallelogram faces. A parallelogram is a quadrilateral whose opposite sides are equal and parallel to each other.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"223\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-parallelepiped-and-a-parallelogram.png\" alt=\"A parallelepiped and a parallelogram\" class=\"wp-image-35828\" title=\"A parallelepiped and a parallelogram\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-parallelepiped-and-a-parallelogram.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-parallelepiped-and-a-parallelogram-300x108.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"1-definition-of-parallelepiped\">Definition of Parallelepiped<\/h2>\n\n\n\n<p><strong>A parallelepiped is a <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/3-dimensional\" target=\"_blank\" rel=\"noopener\" title=\"\"><strong>three-dimensional shape<\/strong><\/a><strong> with parallelogram-like faces. It is a <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polyhedron\" target=\"_blank\" rel=\"noopener\" title=\"\"><strong>polyhedron<\/strong><\/a><strong> since it is made of <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polygon\" target=\"_blank\" rel=\"noopener\" title=\"\"><strong>polygons<\/strong><\/a><strong>. It has sharp corners, straight edges, and polygon faces. It has three pairs of parallel faces joined together.<\/strong><\/p>\n\n\n\n<p>Its special cases are the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/cube\" target=\"_blank\" rel=\"noopener\" title=\"\">cube<\/a> and cuboid. All of the faces of the rectangular parallelepiped are rectangular.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"252\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/cube-and-cuboid-as-parallelepipeds.png\" alt=\"Cube and cuboid as parallelepipeds\" class=\"wp-image-35830\" title=\"Cube and cuboid as parallelepipeds\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/cube-and-cuboid-as-parallelepipeds.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/cube-and-cuboid-as-parallelepipeds-300x122.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-properties-of-parallelepiped\">Properties of Parallelepiped<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>It is a solid figure. It means that it has three dimensions.<\/li>\n\n\n\n<li>A parallelepiped has 6 faces, 12 edges, and 8 vertices.<\/li>\n\n\n\n<li>There are three pairs of parallel faces.<\/li>\n\n\n\n<li>The diagonal of each face refers to the &#8220;face diagonal.&#8221;<\/li>\n\n\n\n<li>From the outside, each face appears to be the mirror image of the opposite face.<\/li>\n\n\n\n<li>It is also referred to as a parallelogram-based prism.<\/li>\n\n\n\n<li>It has six faces. It is a polyhedron made of parallelograms.<\/li>\n\n\n\n<li>It is a hexahedron (a polyhedron with six faces).<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-difference-between-parallelogram-and-parallelepiped\">Difference between Parallelogram and Parallelepiped<\/h2>\n\n\n\n<figure class=\"wp-block-table wj-custom-table\"><table class=\"wj-table-class\"><thead><tr><th><strong>Parallelogram<\/strong><\/th><th><strong>Parallelepiped<\/strong><\/th><\/tr><\/thead><tbody><tr><td><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/06\/table_1.png\" alt=\"Parallelogram\"><\/td><td><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/06\/table_2-1.png\" alt=\"Parallelepiped\"><\/td><\/tr><tr><td>It is a convex quadrilateral in which each pair of opposite edges are parallel and of equal length. It is a 2D figure.<\/td><td>A parallelepiped is a three-dimensional shape with 6 faces, each of which is a parallelogram.<\/td><\/tr><tr><td>Example: <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/square\" target=\"_blank\" rel=\"noopener\" title=\"\">Square<\/a>, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/rectangle\" target=\"_blank\" rel=\"noopener\" title=\"\">Rectangle<\/a>, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/rhombus\" target=\"_blank\" rel=\"noopener\" title=\"\">Rhombus<\/a><\/td><td>Example: Cube, Cuboid, Rhomboid<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-surface-area-of-parallelepiped\">Surface Area of Parallelepiped<\/h2>\n\n\n\n<p>The total area covered by all parallelepiped surfaces is referred to as the parallelepiped&#8217;s total surface area. It means that the total area of the 6 parallelograms forming the faces of a parallelepiped defines the total surface area of the parallelepiped.&nbsp;<\/p>\n\n\n\n<p>A parallelepiped&#8217;s surface area is measured in square units like $in^{2},\\; ft^{2},\\; yard^{2}$, etc. There are two types of parallelepiped surface area:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Lateral surface area<\/li>\n\n\n\n<li>Total surface area&nbsp;<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"360\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/dimensions-of-a-parallelepiped.png\" alt=\"Dimensions of a parallelepiped \" class=\"wp-image-35831\" title=\"Dimensions of a parallelepiped \" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/dimensions-of-a-parallelepiped.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/dimensions-of-a-parallelepiped-300x174.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-lateral-surface-area-of-parallelepiped\">Lateral Surface Area of Parallelepiped<\/h2>\n\n\n\n<p>The area covered by the parallelepiped&#8217;s lateral or side faces is known as its lateral surface area. We determine the sum of the areas of four lateral faces in order to calculate the LSA of a parallelepiped.<\/p>\n\n\n\n<p>In other words, we can say that the surface area of a parallelepiped&#8217;s face, excluding its base and top, is referred to as its lateral surface area.<\/p>\n\n\n\n<p><strong>Lateral Surface Area Formula (Bold)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Lateral surface area (LSA) of parallelepiped $=$ Perimeter of base $\\times$ Height&nbsp;<\/li>\n\n\n\n<li>Lateral surface area (LSA) $= 2(a + b) \\times h$<\/li>\n<\/ul>\n\n\n\n<p>where&nbsp;<\/p>\n\n\n\n<p>a is the length of the base,&nbsp;<\/p>\n\n\n\n<p>b is the breadth of the base,&nbsp;<\/p>\n\n\n\n<p>and&nbsp;<\/p>\n\n\n\n<p>h is the height of parallelepiped.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-total-surface-area-of-parallelepiped\">Total Surface Area of Parallelepiped<\/h2>\n\n\n\n<p>The total area that is covered by all the faces of a parallelepiped is known as the total surface area of the parallelepiped. We find the sum of the areas of all the six faces in order to calculate the TSA of a parallelepiped.<\/p>\n\n\n\n<p><strong>Total Surface Area of Parallelepiped Formula (Bold)<\/strong><\/p>\n\n\n\n<p>The formula for determining the lateral and total surface areas of the parallelepiped is as follows:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total surface area (TSA) $=$ LSA $+ 2$(Base area)&nbsp;<\/li>\n\n\n\n<li>Total surface area (TSA) $= [2(a + b) \\times h] + 2$(Base area)&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>where a is the length, b is the breadth and h is the height of parallelepiped.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-volume-of-parallelepiped\">Volume of Parallelepiped<\/h2>\n\n\n\n<p>The total space that a parallelepiped occupies in a three-dimensional plane is called its volume. It is measured in cubic units like $in^{3},\\; ft^{3},\\; yard^{3}$, and so on.<\/p>\n\n\n\n<p><strong>Parallelepiped Volume Formula (Bold)<\/strong><\/p>\n\n\n\n<p>Let\u2019s understand how to find the volume of a parallelepiped. The volume of the parallelepiped is given by the product the base area and height.<\/p>\n\n\n\n<p><strong>Volume of parallelepiped (V) <\/strong>$=$<strong> Base Area <\/strong>$\\times$<strong> Height<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-parallelepiped-formulas\">Parallelepiped Formulas<\/h2>\n\n\n\n<figure class=\"wp-block-table wj-custom-table\"><table class=\"wj-table-class\"><tbody><tr><td><strong>Lateral Surface Area (LSA)<\/strong><\/td><td>Perimeter of base $\\times$ Height<\/td><\/tr><tr><td><strong>Total Surface Area (TSA)<\/strong><\/td><td>LSA $+ 2$(Base area)&nbsp;<\/td><\/tr><tr><td><strong>Volume (V)<\/strong><\/td><td>Base Area $\\times$ Height<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-rectangular-parallelepiped\">Rectangular Parallelepiped<\/h2>\n\n\n\n<p>A unique parallelepiped, with all six faces being rectangular in shape, is the rectangular parallelepiped, which is also known as a cuboid. All of the parallel edges have the same length. A typical rectangular parallelepiped is a shoebox.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"333\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rectangular-parallelepiped.png\" alt=\"Rectangular parallelepiped\" class=\"wp-image-35832\" title=\"Rectangular parallelepiped\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rectangular-parallelepiped.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rectangular-parallelepiped-300x161.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total surface area (TSA) $= 2(lb + bh + lh)$&nbsp;<\/li>\n\n\n\n<li>Volume (V) $= l \\times b \\times h$<\/li>\n\n\n\n<li>Diagonal (D) $= \\sqrt{l^{2} + b^{2} + h^{2}}$<\/li>\n<\/ul>\n\n\n\n<p>Where l, b, and h are the three dimensions.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-facts-about-parallelepipeds\">Facts about Parallelepipeds<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Specific types of parallelepipeds include the rectangular cuboid with six rectangular faces, the cube with six square faces, and the rhombohedron with six rhombus faces.<\/li>\n\n\n\n<li>A prism whose base is a parallelogram is referred to as the parallelepiped.<\/li>\n\n\n\n<li>The length of the parallel edges of a parallelepiped is the same.<\/li>\n\n\n\n<li>The rectangular parallelepiped has three distinct faces that can be seen at the same time.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about parallelepiped and rectangular parallelepiped shapes, their properties, formulas for surface area and volume. Let\u2019s solve a few examples and practice problems on parallelepiped.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-solved-examples-on-parallelepipeds\">Solved Examples on Parallelepipeds<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Find the parallelepiped&#8217;s lateral surface area if its base face has opposite sides measuring 5 inches by 7 inches and a height of 6 inches.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>a $= 5$ inches and b $= 7$ inches<\/p>\n\n\n\n<p>height $= 6$ inches<\/p>\n\n\n\n<p>Applying the lateral surface area of the parallelepiped formula,<\/p>\n\n\n\n<p>$\\Rightarrow LSA = 2(a + b) \\times h$<\/p>\n\n\n\n<p>$\\Rightarrow LSA = 2(5 + 7) \\times 6 = 144\\; inches^{2}$<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>The sides of a parallelepiped&#8217;s base are given by 7 feet and 11 feet, respectively. The parallelepiped has a height of 8 feet. Find out how much it would cost to paint its lateral walls for <\/strong>$\\$20$<strong> per square foot.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>$a = 7$ feet, $b = 11$ feet<\/p>\n\n\n\n<p>To find the cost to paint its side walls, first, we have to find the lateral surface area.<\/p>\n\n\n\n<p>Applying the lateral surface area of the parallelepiped formula,<\/p>\n\n\n\n<p>$ LSA = 2(a + b) \\times h$<\/p>\n\n\n\n<p>$\\Rightarrow LSA = 2(7 + 11) \\times 8 = 288$ sq. feet.<\/p>\n\n\n\n<p>Now,<\/p>\n\n\n\n<p>The cost of painting exterior walls $=$ Lateral surface area $\\times$ cost per square foot.<\/p>\n\n\n\n<p>$\\therefore$ The cost of painting exterior walls $= 288 \\times \\$20 = \\$5,760$<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>A rectangular box has dimensions 5 in <\/strong>$\\times$<strong> 4 in <\/strong>$\\times$<strong> 3 in. Find the total surface area.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>The dimensions of a rectangular box are 5 in $\\times$ 4 in $\\times$ 3 in.<\/p>\n\n\n\n<p>length (a) $= 5$ in, width (b) $= 4$ in, and height (h) $= 3$ in<\/p>\n\n\n\n<p>Total surface area (TSA) $= 2(a \\times b + b \\times c + c \\times a)$<\/p>\n\n\n\n<p>$\\Rightarrow TSA = 2 (5 \\times 4 + 4 \\times 3 + 3 \\times 5)$<\/p>\n\n\n\n<p>$\\Rightarrow TSA = 2 (20 + 12 + 15)$<\/p>\n\n\n\n<p>$\\Rightarrow TSA = 94\\; in^{2}$.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li><strong>&nbsp;If the base area of a parallelepiped is <\/strong>$70\\;in^{2}$<strong> and the height is 8 inches, then find its volume.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The base area of a parallelepiped $= 70\\; in^{2}$, height $= 8$ inches.<\/p>\n\n\n\n<p>The volume of parallelepiped (V) $=$ Base Area $\\times$ Height<\/p>\n\n\n\n<p>$V = 70 \\times 8 = 560\\; in^{3}$.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li><strong>&nbsp;A rectangular parallelepiped has dimensions of 10 in, 5 in, and 4 in. Find the length of its diagonal.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>a $= 10$ in, b $= 5$ in, and c $= 4$ in.<\/p>\n\n\n\n<p>The diagonal of rectangular parallelepiped $= \\sqrt{a^{2} + b^{2} + c^{2}}$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\sqrt{10^{2} + 5^{2} + 4^{2}}$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\sqrt{141}$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 11.87$ in<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-practice-problems-on-parallelepipeds\">Practice Problems on Parallelepipeds<\/h2>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"14-frequently-asked-questions-on-parallelepipeds\">Frequently Asked Questions on Parallelepipeds<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-742ad21b-d374-4802-a5a6-f3d5852b4d67\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-742ad21b-d374-4802-a5a6-f3d5852b4d67\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-742ad21b-d374-4802-a5a6-f3d5852b4d67\"><strong>How many edges and vertices does a parallelepiped have?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-742ad21b-d374-4802-a5a6-f3d5852b4d67\">\n\n<p>A parallelepiped has 12 edges and 8 vertices.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-742ad21b-d374-4802-a5a6-f3d5852b4d67\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-742ad21b-d374-4802-a5a6-f3d5852b4d67\"><strong>What is a rectangular parallelepiped?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-742ad21b-d374-4802-a5a6-f3d5852b4d67\">\n\n<p>A unique parallelepiped with all six faces being rectangular is the rectangular parallelepiped, which is also known as a cuboid.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-742ad21b-d374-4802-a5a6-f3d5852b4d67\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-742ad21b-d374-4802-a5a6-f3d5852b4d67\"><strong>What are the rectangular parallelepiped formulas?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-742ad21b-d374-4802-a5a6-f3d5852b4d67\">\n\n<p>The formula for calculating surface areas and volume for rectangular parallelepiped are as follows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total surface area (TSA) $= 2(a \\times b + b \\times c + c \\times a)$<\/li>\n\n\n\n<li>Volume (V) $= a \\times b \\times c$,<\/li>\n\n\n\n<li>Diagonal (D) $= \\sqrt{a^{2} + b^{2} + c^{2}}$<\/li>\n<\/ul>\n\n\n\n<p>where a, b, and c are the three dimensions.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-742ad21b-d374-4802-a5a6-f3d5852b4d67\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-742ad21b-d374-4802-a5a6-f3d5852b4d67\"><strong>What is the shape of a parallelepiped?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-742ad21b-d374-4802-a5a6-f3d5852b4d67\">\n\n<p>A parallelepiped is a three-dimensional shape with 6 parallelogram-like faces. It is a polyhedron, which means that it has six faces. It is made up of three pairs of parallel faces joined together. Its special cases are the cube and cuboid etc.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-742ad21b-d374-4802-a5a6-f3d5852b4d67\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-742ad21b-d374-4802-a5a6-f3d5852b4d67\"><strong>What are the real-life examples of a parallelepiped shape?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-742ad21b-d374-4802-a5a6-f3d5852b4d67\">\n\n<p>Some real-life examples of parallelepiped shapes are shoeboxes, bricks, cubes, etc.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-742ad21b-d374-4802-a5a6-f3d5852b4d67\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-742ad21b-d374-4802-a5a6-f3d5852b4d67\"><strong>Is a rectangle a parallelepiped?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-742ad21b-d374-4802-a5a6-f3d5852b4d67\">\n\n<p>No, a rectangle is a 2D shape, whereas a parallelepiped is a 3D shape (a polyhedron) where each face is a parallelogram.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-6-742ad21b-d374-4802-a5a6-f3d5852b4d67\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-742ad21b-d374-4802-a5a6-f3d5852b4d67\"><strong>Is a cube a parallelepiped?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-6-742ad21b-d374-4802-a5a6-f3d5852b4d67\">\n\n<p>A cube is a parallelepiped where each face is a square.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is a Parallelepiped in Math? A parallelepiped is a three-dimensional geometric solid with six faces such that each face is a parallelogram. It is also called a prism with a parallelogram base. A parallelepiped is a polyhedron since it is formed by 6 parallelogram faces. A parallelogram is a quadrilateral whose opposite sides are &#8230; <a title=\"Parallelepiped: Definition, Formula, Volume, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/parallelepiped\" aria-label=\"More on Parallelepiped: Definition, Formula, Volume, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-30304","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/30304","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=30304"}],"version-history":[{"count":15,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/30304\/revisions"}],"predecessor-version":[{"id":35833,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/30304\/revisions\/35833"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=30304"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=30304"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=30304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}