{"id":623053,"date":"2023-06-20T22:38:58","date_gmt":"2023-06-20T17:08:58","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=623053"},"modified":"2024-11-21T17:55:55","modified_gmt":"2024-11-21T12:25:55","slug":"volume-of-parallelepiped-formula","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/","title":{"rendered":"Volume of Parallelepiped Formula\u00a0"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#Volume_of_Parallelepiped_Formula\" title=\"Volume of Parallelepiped Formula \">Volume of Parallelepiped Formula <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#Introduction_to_Volume_of_Parallelepiped_Formula\" title=\"Introduction to Volume of Parallelepiped Formula \">Introduction to Volume of Parallelepiped Formula <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#What_Is_a_Parallelepiped\" title=\"What Is a Parallelepiped? \">What Is a Parallelepiped? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#Properties_of_Parallelepiped\" title=\"Properties of Parallelepiped \">Properties of Parallelepiped <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#Volume_of_Parallelepiped\" title=\"Volume of Parallelepiped \">Volume of Parallelepiped <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#Volume_of_Parallelepiped_Formula-2\" title=\"Volume of Parallelepiped Formula \">Volume of Parallelepiped Formula <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#Solved_Examples_on_Volume_of_Parallelepiped_Formula\" title=\"Solved Examples on Volume of Parallelepiped Formula  \">Solved Examples on Volume of Parallelepiped Formula  <\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#Frequently_Asked_Questions_on_Volume_of_Parallelepiped_Formula\" title=\"Frequently Asked Questions on Volume of Parallelepiped Formula  \">Frequently Asked Questions on Volume of Parallelepiped Formula  <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#What_Is_Meant_By_a_Parallelepiped\" title=\"What Is Meant By a Parallelepiped? \">What Is Meant By a Parallelepiped? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#What_Is_the_Volume_of_a_Parallelepiped\" title=\"What Is the Volume of a Parallelepiped?\">What Is the Volume of a Parallelepiped?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#What_Is_the_Total_Surface_Area_of_a_Parallelepiped\" title=\"What Is the Total Surface Area of a Parallelepiped?\">What Is the Total Surface Area of a Parallelepiped?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#What_Is_the_Lateral_Surface_Area_of_a_Parallelepiped\" title=\"What Is the Lateral Surface Area of a Parallelepiped? \">What Is the Lateral Surface Area of a Parallelepiped? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#What_Is_a_Rectangular_Parallelepiped\" title=\"What Is a Rectangular Parallelepiped?\">What Is a Rectangular Parallelepiped?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#What_Is_the_Shape_of_a_Parallelepiped\" title=\"What Is the Shape of a Parallelepiped? \">What Is the Shape of a Parallelepiped? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/volume-of-parallelepiped-formula\/#How_do_you_find_the_base_area_of_a_parallelepiped\" title=\"How do you find the base area of a parallelepiped? \">How do you find the base area of a parallelepiped? <\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span style=\"font-size: 18pt;\"><b>Volume of Parallelepiped Formula<\/b> <\/span><\/h2>\n<h2><span style=\"font-size: 14pt;\"><b>Introduction to Volume of Parallelepiped Formula<\/b> <\/span><\/h2>\n<p><span data-contrast=\"auto\">A parallelepiped is a three-dimensional shape that is formed by six parallelograms. The word &#8216;parallelepiped&#8217; is derived from the Greek word parallelepipdon, meaning &#8220;a body having parallel bodies&#8221;. We can say that a parallelepiped relates with a parallelogram just like a cube relates with a square. Parallelepiped has 6 parallelogram-shaped faces, 8 vertices, and 12 edges. Let us understand properties and different formulas associated with a surface area and volume of a parallelepiped in the following sections.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">What Is a Parallelepiped?<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">A parallelepiped is a<strong> three-dimensional shape<\/a><\/strong> with six faces, that are all in the shape of a parallelogram. It has 6 faces, 8 vertices, and 12 edges. Cube, cuboid, and rhomboid are all special cases of a parallelepiped. A cube is a <strong><a href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelepiped\/\" target=\"_blank\" rel=\"noopener\">parallelepiped<\/a><\/strong> whose all sides are square-shaped. Similarly, a cuboid and a rhomboid are parallelepipeds with rectangle and rhombus-shaped faces respectively. In the figure given below, we can observe a parallelepiped, with &#8216;a&#8217;, &#8216;b&#8217;, and &#8216;c&#8217; as side lengths and &#8216;h&#8217; as the height of the parallelepiped.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-medium wp-image-623065 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-223829-300x165.png\" alt=\"\" width=\"300\" height=\"165\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-223829-300x165.png?v=1687280929 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-223829.png?v=1687280929 706w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Properties of Parallelepiped<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">There are certain properties of a parallelepiped that help us distinguish it from other 3-D shapes. These properties are listed below,<\/span> <span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ul>\n<li><span data-contrast=\"auto\">Parallelepiped is a three-dimensional solid shape.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">It has 6 faces, 12 edges, and 8 vertices.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">All faces of a parallelepiped are in the shape of a parallelogram.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">A parallelepiped has 2 diagonals on each face, called the face diagonals. It has a total of 12 face diagonals.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">The diagonals connecting the vertices not lying on the same face are called the body or space diagonal of a parallelepiped.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">Parallelepiped is referred to as a prism with a parallelogram-shaped base.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">Each face of a parallelepiped is a mirror image of the opposite face.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ul>\n<h2><b><span data-contrast=\"auto\">Volume of Parallelepiped<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">The volume of a parallelepiped is defined as the space occupied by the shape in a three-dimensional plane. The volume of a parallelepiped is expressed in cubic units, like in<\/span><span data-contrast=\"auto\">3<\/span><span data-contrast=\"auto\">, cm<\/span><span data-contrast=\"auto\">3<\/span><span data-contrast=\"auto\">, m<\/span><span data-contrast=\"auto\">3<\/span><span data-contrast=\"auto\">, ft<\/span><span data-contrast=\"auto\">3<\/span><span data-contrast=\"auto\">, yd<\/span><span data-contrast=\"auto\">3<\/span><span data-contrast=\"auto\">, etc.<\/span><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Volume of Parallelepiped Formula<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">Volume of parallelepiped can be calculated using the base area and the height. The formula to calculate the volume of a parallelepiped is given as,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">V = B \u00d7 H<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">where,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">B = Base area<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">H = Height of parallelepiped<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Solved Examples on Volume of Parallelepiped Formula<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><b><span data-contrast=\"auto\">Example 1: <\/span><\/b><span data-contrast=\"auto\">If the base face of a parallelepiped has opposite sides measuring 6 inches and 10 inches and its height is 7 inches, find the lateral surface area of the parallelepiped.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Using the lateral area of parallelepiped formula,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">LSA = Perimeter of base \u00d7 height<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">\u21d2 LSA = 2(6 + 10) \u00d7 7 = 224 in<\/span><span data-contrast=\"auto\">2<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Lateral area of given parallelepiped = 224 in<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <strong>Ex<\/strong><\/span><b><span data-contrast=\"auto\">ample 2:<\/span><\/b><span data-contrast=\"auto\"> A gift is packed in a rectangular box of dimensions 10 in, 7 in, and 8 in and it needs to be wrapped with gift paper. How much gift paper is required to wrap the gift box?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><strong>Solution: <\/strong><\/p>\n<p><span data-contrast=\"auto\"> The dimensions of the given gift box are,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">length, l = 10 in<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">width, w = 7 in<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">height, h = 8 in<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">To find the amount of gift paper required, we need to find the total surface area of the box. Since the shape of the box can be compared to a rectangular parallelepiped,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">TSA = 2 (lw + wh + hl)<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">        = 2 (10 \u00d7 7 + 7 \u00d7 8 + 8 \u00d7 10)<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">        = 2 (70 + 56 + 80)<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">        = 412 in<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The amount area of the gift paper required = 412 in<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h4><span style=\"font-size: 14pt;\"><b>Frequently Asked Questions on Volume of Parallelepiped Formula<\/b>  <\/span><\/h4>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h4><span class=\"ez-toc-section\" id=\"What_Is_Meant_By_a_Parallelepiped\"><\/span>What Is Meant By a Parallelepiped? <span class=\"ez-toc-section-end\"><\/span><\/h4>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tParallelepiped is a three-dimensional shape with 6 parallelogram-shaped faces, 12 edges, and 8 vertices. Parallelepiped is often referred to as a prism with a parallelogram-shaped base. Cube, cuboid, and rhomboid are all special cases of a parallelepiped with faces of the shape of a square, rectangle, and rhombus respectively.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h4><span class=\"ez-toc-section\" id=\"What_Is_the_Volume_of_a_Parallelepiped\"><\/span>What Is the Volume of a Parallelepiped?<span class=\"ez-toc-section-end\"><\/span><\/h4>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe volume of a parallelepiped is the capacity or the shape or the total space occupied in a three-dimensional plane. The volume of the parallelepiped by cubic units, like in3, cm3, ft3, in3, etc. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h4><span class=\"ez-toc-section\" id=\"What_Is_the_Total_Surface_Area_of_a_Parallelepiped\"><\/span>What Is the Total Surface Area of a Parallelepiped?<span class=\"ez-toc-section-end\"><\/span><\/h4>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe total surface area of a parallelepiped is the area covered by all the faces of a parallelepiped. It is expressed in square units, like in2, m2, cm2, ft2, etc. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h4><span class=\"ez-toc-section\" id=\"What_Is_the_Lateral_Surface_Area_of_a_Parallelepiped\"><\/span>What Is the Lateral Surface Area of a Parallelepiped? <span class=\"ez-toc-section-end\"><\/span><\/h4>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe lateral surface area of a parallelepiped is the area or region covered by all the lateral or side faces of a parallelepiped. It is expressed in square units, using units like square inches, square meters, square feet, etc. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h4><span class=\"ez-toc-section\" id=\"What_Is_a_Rectangular_Parallelepiped\"><\/span>What Is a Rectangular Parallelepiped?<span class=\"ez-toc-section-end\"><\/span><\/h4>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA rectangular parallelepiped is a type of parallelepiped whose all six faces are in a rectangular shape and the length of the parallel edges are equal.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h4><span class=\"ez-toc-section\" id=\"What_Is_the_Shape_of_a_Parallelepiped\"><\/span>What Is the Shape of a Parallelepiped? <span class=\"ez-toc-section-end\"><\/span><\/h4>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tParallelopiped is a 3-D shape that has all the sides in the shape of a parallelogram. The opposite faces of a parallelepiped are mirror images of eachother.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h4><span class=\"ez-toc-section\" id=\"How_do_you_find_the_base_area_of_a_parallelepiped\"><\/span>How do you find the base area of a parallelepiped? <span class=\"ez-toc-section-end\"><\/span><\/h4>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe three pairs of parallel faces form a hexahedron. For a given parallelepiped, let S is the area of the bottom face and H is the height, then the volume formula is given by; Since the base of parallelepiped is in the shape of a parallelogram, therefore we can use the formula for the area of the parallelogram to find the base area.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What Is Meant By a Parallelepiped? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Parallelepiped is a three-dimensional shape with 6 parallelogram-shaped faces, 12 edges, and 8 vertices. Parallelepiped is often referred to as a prism with a parallelogram-shaped base. Cube, cuboid, and rhomboid are all special cases of a parallelepiped with faces of the shape of a square, rectangle, and rhombus respectively.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What Is the Volume of a Parallelepiped?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The volume of a parallelepiped is the capacity or the shape or the total space occupied in a three-dimensional plane. The volume of the parallelepiped by cubic units, like in3, cm3, ft3, in3, etc.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What Is the Total Surface Area of a Parallelepiped?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The total surface area of a parallelepiped is the area covered by all the faces of a parallelepiped. It is expressed in square units, like in2, m2, cm2, ft2, etc.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What Is the Lateral Surface Area of a Parallelepiped? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The lateral surface area of a parallelepiped is the area or region covered by all the lateral or side faces of a parallelepiped. It is expressed in square units, using units like square inches, square meters, square feet, etc.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What Is a Rectangular Parallelepiped?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A rectangular parallelepiped is a type of parallelepiped whose all six faces are in a rectangular shape and the length of the parallel edges are equal.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What Is the Shape of a Parallelepiped? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Parallelopiped is a 3-D shape that has all the sides in the shape of a parallelogram. The opposite faces of a parallelepiped are mirror images of eachother.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How do you find the base area of a parallelepiped? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The three pairs of parallel faces form a hexahedron. For a given parallelepiped, let S is the area of the bottom face and H is the height, then the volume formula is given by; Since the base of parallelepiped is in the shape of a parallelogram, therefore we can use the formula for the area of the parallelogram to find the base area.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n<p><span data-contrast=\"auto\">What Are the Parallelepiped Formulas?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: The formulas associated with a parallelepiped are given as,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"auto\"> LSA of parallelepiped = P \u00d7 H<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"auto\">TSA of parallelepiped = (P \u00d7 H) + (2 \u00d7 B)<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"3\" data-aria-level=\"1\"><span data-contrast=\"auto\">Volume of parallelepiped = B \u00d7 H<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">where, B is the base area, H is the height of the parallelepiped, and P is the perimeter of base.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Volume of Parallelepiped Formula Introduction to Volume of Parallelepiped Formula A parallelepiped is a three-dimensional shape that is formed by [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Volume of Parallelepiped Formula","_yoast_wpseo_title":"Volume of Parallelepiped Formula with Examples - Infinity learn","_yoast_wpseo_metadesc":"Calculate the volume of a parallelepiped using the formula: base area x height. 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