{"id":623070,"date":"2023-06-20T22:40:42","date_gmt":"2023-06-20T17:10:42","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=623070"},"modified":"2025-02-28T18:03:56","modified_gmt":"2025-02-28T12:33:56","slug":"surface-area-of-a-pyramid-formula","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/formulas\/surface-area-of-a-pyramid-formula\/","title":{"rendered":"Surface Area of a Pyramid 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\/surface-area-of-a-pyramid-formula\/#Introduction_to_Surface_Area_of_a_Pyramid_Formula\" title=\"Introduction to Surface Area of a Pyramid Formula \">Introduction to Surface Area of a Pyramid 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\/surface-area-of-a-pyramid-formula\/#What_is_the_Surface_Area_of_Pyramid\" title=\"What is the Surface Area of Pyramid? \">What is the Surface Area of Pyramid? <\/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\/surface-area-of-a-pyramid-formula\/#Surface_Area_of_Pyramid_Formula\" title=\"Surface Area of Pyramid Formula \">Surface Area of Pyramid Formula <\/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\/surface-area-of-a-pyramid-formula\/#Proof_of_Surface_Area_of_Pyramid_Formula\" title=\"Proof of Surface Area of Pyramid Formula \">Proof of Surface Area of Pyramid Formula <\/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\/surface-area-of-a-pyramid-formula\/#Surface_Area_of_Pyramid_with_Altitude\" title=\"Surface Area of Pyramid with Altitude \">Surface Area of Pyramid with Altitude <\/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\/surface-area-of-a-pyramid-formula\/#Solved_Examples_on_Surface_Area_of_a_Pyramid_Formula\" title=\"Solved Examples on Surface Area of a Pyramid Formula \">Solved Examples on Surface Area of a Pyramid 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\/surface-area-of-a-pyramid-formula\/#Frequently_Asked_Questions_on_Surface_Area_of_a_Pyramid_Formula\" title=\"Frequently Asked Questions on Surface Area of a Pyramid Formula \">Frequently Asked Questions on Surface Area of a Pyramid Formula <\/a><\/li><\/ul><\/nav><\/div>\n<h2><b><span data-contrast=\"auto\">Introduction to Surface Area of a Pyramid 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\">The surface area of a pyramid is obtained by adding the area of all its faces. A pyramid is a three-dimensional shape whose base is a polygon and whose side faces (that are triangles) meet at a point which is called the apex (or) vertex. The perpendicular distance from the apex to the center of the base is called the altitude or height of the pyramid. The length of the perpendicular drawn from the apex to the base of a triangle (side face) is called the &#8216;slant height&#8217;. Let us learn more about the surface area of a pyramid along with its formula, and a few solved examples.<\/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<h2><b><span data-contrast=\"auto\">What is the Surface Area of Pyramid?<\/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 surface area of a pyramid is a measure of the total area that is occupied by all its faces. Observe the pyramid given below to see all its faces and the other parts like the apex, the altitude, the slant height, and the 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}\"><img loading=\"lazy\" class=\"size-medium wp-image-623082 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-224013-300x208.png\" alt=\"\" width=\"300\" height=\"208\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-224013-300x208.png?v=1687281031 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-20-224013.png?v=1687281031 646w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/> <\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span data-contrast=\"auto\">The surface area of a pyramid is the sum of areas of its faces and hence it is measured in square units such as m<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, cm<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, in<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, ft<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\">, etc. A pyramid has two types of surface areas, one is the Lateral Surface Area (LSA) and the other is the Total Surface Area (TSA).<\/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\"> <\/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=\"1\" 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\">The Lateral Surface Area (LSA) of a pyramid = The sum of areas of the side faces (triangles) of the pyramid.<\/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=\"1\" 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\">The Total Surface Area (TSA) of a pyramid = LSA of pyramid + 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><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">In general, the surface area of a pyramid without any specifications refers to the total surface area of the pyramid.<\/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<h2><b><span data-contrast=\"auto\">Surface Area of Pyramid 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\">The surface area of a pyramid can be calculated by finding the areas of each of its faces and adding them. If the pyramid is regular (i.e., a pyramid whose base is a regular polygon and whose altitude passes through the center of the base), there are some specific formulas to find the lateral surface area and total surface 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\">Consider a regular pyramid whose base perimeter is &#8216;P&#8217;, the base area is &#8216;B&#8217;, and slant height (the height of each triangle) is &#8216;l&#8217;. Then,<\/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\">The Lateral Surface Area of pyramid (LSA) = (1\/2) Pl<\/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\">The Total Surface Area of pyramid (TSA) = LSA + base area = (1\/2) Pl + 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<\/ul>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Proof of Surface Area of Pyramid Formula<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">The surface area of a pyramid involves the perimeter and slant height. Let us understand the formulas of LSA and TSA of a pyramid by taking a specific pyramid as an example. Let us consider a square pyramid whose base length is &#8216;a&#8217; and whose slant height is &#8216;l&#8217;.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Then,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"3\" 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\"> The base area (area of square) of the pyramid is, B = a<\/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><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"3\" 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\">The base perimeter (perimeter of square) of the pyramid is, P = 4a<\/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<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"3\" 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\">The area of each of the side faces (area of triangle) = (1\/2) \u00d7 base \u00d7 height = (1\/2) \u00d7 (a) \u00d7 l<\/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\">Therefore, the sum of all side faces (sum of all 4 triangular faces) = 4 [(1\/2) \u00d7 (a) \u00d7 l] = (1\/2) \u00d7 (4a) \u00d7 l = (1\/2) Pl. (Here, we replaced 4a with P which represents its perimeter.)<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&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;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Hence, the Lateral Surface Area of the pyramid (LSA) = (1\/2) Pl<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> We know that the Total Surface Area of a pyramid (TSA) is obtained by adding the base and lateral surface areas. Thus,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The total surface area of pyramid (TSA) = LSA + base area = (1\/2) Pl + B<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Using these two formulas, we can derive the surface area formulas of different types of pyramids.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Surface Area of Pyramid with Altitude<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The surface area of a pyramid can be calculated if its altitude is given. Observe the figure given below which shows that the triangle formed by half the side length of the base (a\/2), the slant height (l), and the altitude (h) is a right-angled triangle. Hence, we can apply the Pythagoras theorem and find out the slant height if the altitude and base length is given. Thus, l<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> = h<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> + (a\/2)<\/span><span data-contrast=\"auto\">2<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"> <\/span><span data-contrast=\"none\">So, we can calculate the slant height using the formula, l<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\"> = h<\/span><span data-contrast=\"none\">2 <\/span><span data-contrast=\"none\">+ (a\/2)<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\">. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Now that we have the slant height, the base length, and the height, we can find the surface area of the pyramid using the formula, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Total surface area of pyramid (TSA) = LSA + base area = (1\/2) Pl + B<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&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;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"none\">Solved Examples on Surface Area of a Pyramid Formula<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">Example 1:<\/span><\/b><span data-contrast=\"none\"> Calculate the lateral surface area of a square pyramid if the side length of the base is 14 inches and the slant height of the pyramid is 20 inches.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Solution:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The side length of the base, a = 14 inches<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Then, the perimeter of the base (square) is, P = 4a = 4(14) = 56 inches.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Slant height, l = 20 inches<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The lateral surface area of a square pyramid is,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Lateral surface area (LSA) = (1\/2) Pl<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">                                               = (1\/2) \u00d7 (56) \u00d7 20<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">                                               = 560 in<\/span><span data-contrast=\"none\">2<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Therefore, the lateral surface area of the given pyramid is 560 in<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\">.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">Example 2: <\/span><\/b><span data-contrast=\"none\">State true or false.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">a.) The surface area of any pyramid can be calculated by finding the areas of each of its faces and adding them.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">b.) The total surface area (TSA) of a pyramid = Lateral Surface Area (LSA) of the pyramid<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Solution:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">a.) True, the surface area of any pyramid can be calculated by finding the areas of each of its faces and adding them.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">b.) False, the total surface area (TSA) of a pyramid = Lateral Surface Area (LSA) of the pyramid + Base area<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">Example 3:<\/span><\/b><span data-contrast=\"none\"> Calculate the total surface area of a square pyramid if the side of the base is given as 14 inches and the height (altitude) of the pyramid is given as 24 inches.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Solution:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Given, the side of the base is, a = 14 inches, and the height of the pyramid is, h = 24 inches.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Let its slant height be &#8216;l&#8217;.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">By Pythagoras theorem, l<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\"> = (a\/2)<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\"> + h<\/span><span data-contrast=\"none\">2<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">l<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\"> = (14\/2)<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\"> + 24<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\"> = 625<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Thus, l = 25 inches.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The perimeter of the base is, P = 4a = 4(14) = 56 inches.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The base area is, B = 142 = 196 square inches.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The total surface area of the square pyramid is,<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">TSA = (1\/2) Pl + B in which B = 196, P = 56, l = 25<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">TSA = [(1\/2) \u00d7 56 \u00d7 25] + 196 = 896 square inches<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Therefore, the TSA of the given pyramid = 896 square inches.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&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;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"none\">Frequently Asked Questions on Surface Area of a Pyramid Formula<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">1: What is the Definition of Surface Area of Pyramid?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: The surface area of a pyramid is defined as the sum of the areas of all its faces. There are two types of surface areas &#8211; the Total Surface Area (TSA), which is the sum of the areas of all the faces, and the other is the Lateral Surface Area (LSA), which is the sum of the areas of the side faces.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">2: What is the Total Surface Area of Pyramid?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: The total surface area of a pyramid is obtained by adding the area of all its faces (both the base and the side faces). The total surface area of a pyramid whose base perimeter is &#8216;P&#8217;, the base area is &#8216;B&#8217;, and slant height is &#8216;l&#8217; is calculated using the formula <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">TSA = (1\/2) Pl + B.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">3: What is the Lateral Surface Area of Pyramid?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: The lateral surface area of a pyramid is the sum of the areas of all its side faces (which are triangles). The lateral surface area of a pyramid is calculated using the formula LSA = (1\/2) Pl, where &#8216;P&#8217; is the perimeter of the base and &#8216;l&#8217; is the slant height.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">4: What is the Formula for Surface Area of Pyramid?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: There are two types of surface areas of a pyramid, one is the total surface area and the other is the lateral surface area. The formula that is used to find these two areas is given below.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Total surface area = (1\/2) Pl + B<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Lateral surface area = (1\/2) Pl<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">where &#8216;B&#8217; is the base area, &#8216;l&#8217; is the slant height, and &#8216;P&#8217; is the base perimeter.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">5: How to Find Surface Area of Pyramid with Slant Height?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: The formula which is used to find the surface area of a pyramid can be calculated using the slant height. Its total surface area can be calculated using the formula, <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">(1\/2) Pl + B. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Consider a pyramid whose slant height is &#8216;l&#8217;, the base perimeter is &#8216;P&#8217;, and the base area is &#8216;B&#8217;. The base area can be found by applying the formulas of the area of a polygon.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\"> <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">6: How to Find the Surface Area of Pyramid with Height (or Altitude)?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: The surface area of a pyramid can be calculated if the altitude is given. Let us consider a pyramid whose base is a regular polygon of side length &#8216;a&#8217;, the slant height of the pyramid is &#8216;l&#8217; and its altitude is &#8216;h&#8217;. Now, if only &#8216;a&#8217; and &#8216;h&#8217; are given and we need to find the surface area, then we need to find the slant height first. Let us understand this using the following steps.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"4\" 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=\"none\">Step 1: Find &#8216;l&#8217; using the Pythagoras theorem, l<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\"> = (a\/2)<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\"> + h<\/span><span data-contrast=\"none\">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><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"4\" 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=\"none\">Step 2: Find the base perimeter &#8216;P&#8217;.<\/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<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"4\" 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=\"none\">Step 3: Find the base area &#8216;B&#8217;.<\/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=\"4\" 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=\"none\">Step 4: Find the total surface area of the pyramid using the formula (1\/2) Pl + 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<\/ul>\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-contrast=\"none\">7: What is the base area of a square pyramid?<\/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=\"none\">Answer: The base of a square pyramid is a square. Hence, the base area of the square pyramid of base edge a is a<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\">.<\/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;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">8: How do you calculate the volume of a pyramid?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Answer: The volume of a pyramid is measured in cubic units and the formula used to calculate the volume of a pyramid is: Volume of a Pyramid = 1\/3 \u00d7 Base Area \u00d7 Height<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction to Surface Area of a Pyramid Formula The surface area of a pyramid is obtained by adding the area [&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":"Surface Area of a Pyramid Formula\u00a0","_yoast_wpseo_title":"Surface Area of a Pyramid Formula\u00a0with Examples - Infinity learn","_yoast_wpseo_metadesc":"Get a clear explanation of the surface area of a pyramid formula. 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