{"id":4361,"date":"2022-01-23T19:54:38","date_gmt":"2022-01-23T19:54:38","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=4361"},"modified":"2022-01-23T19:54:38","modified_gmt":"2022-01-23T19:54:38","slug":"surface-area-of-pyramids","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/surface-area-of-pyramids\/","title":{"rendered":"Surface Area of Pyramids"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″ css=”.vc_custom_1633761494145{border-radius: 1px !important;}”][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Surface Area of Pyramids<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The surface area of a pyramid is obtained by adding the areas of its faces. A pyramid is a three-dimensional shape whose base is a polygon and whose side faces (that are triangles) all 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 “slant height”.<\/p>\n<p>The surface area of a pyramid is a measure of the total area that is occupied by the surface. In other words, it’s the sum of areas of its faces and hence it is measured in square units such as m<sup>2<\/sup>, cm<sup>2<\/sup>, in<sup>2<\/sup>, ft<sup>2<\/sup>, etc. A pyramid has two types of surface areas, one is lateral surface area (LSA) and the other is the total surface area (TSA).<\/p>\n<p><strong>The lateral surface area (LSA) of a pyramid<\/strong> = The sum of areas of the side faces (triangles) of the pyramid.<br \/>\n<strong>The total surface area (TSA) of a pyramid<\/strong> = LSA of pyramid + Base area.<br \/>\nIn general, the surface area of a pyramid without any specifications means the total surface area of the pyramid.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-pyramids\"><img loading=\"lazy\" class=\"alignnone wp-image-5889 size-medium\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/sf-300x281.png\" alt=\"\" width=\"300\" height=\"281\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/sf-300x281.png 300w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/sf.png 422w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><br \/>\n1. Determine the area of the base (B) and the perimeter of the base (B).<br \/>\n2. Find the slant height (B).<br \/>\n3. Use those values in the formula, <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;S.A.&space;=B&space;+\\frac{1}{2}Pl\" alt=\"\\fn_phv S.A. =B +\\frac{1}{2}Pl\" align=\"absmiddle\" \/><br \/>\n4.State the total surface area in the appropriate square units.<\/p>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<span style=\"color: #16a085;\"><strong>Calculate the surface area of the pyramid shown below.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-pyramids\"><img loading=\"lazy\" class=\"alignnone wp-image-4365 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/2-41.png\" alt=\"\" width=\"173\" height=\"208\" \/><\/a><br \/>\n<\/strong><\/span>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;S.A.&space;=&space;Base\\;area+\\frac{1}{2}(Perimeter)(Length)\" alt=\"\\fn_phv S.A. = Base\\;area+\\frac{1}{2}(Perimeter)(Length)\" align=\"absmiddle\" \/><\/p>\n<p>or, <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;S.A.&space;=&space;B+\\frac{1}{2}Pl\" alt=\"\\fn_phv S.A. = B+\\frac{1}{2}Pl\" align=\"absmiddle\" \/><\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;S.A.&space;=&space;5^{2}+\\frac{1}{2}(4\\times5)\\times&space;11\" alt=\"\\fn_phv S.A. = 5^{2}+\\frac{1}{2}(4\\times5)\\times 11\" align=\"absmiddle\" \/><\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;S.A.&space;=&space;25+110\" alt=\"\\fn_phv S.A. = 25+110\" align=\"absmiddle\" \/><\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;{\\color{Red}&space;S.A.&space;=&space;135\\;m^{2}}\" alt=\"\\fn_phv {\\color{Red} S.A. = 135\\;m^{2}}\" align=\"absmiddle\" \/>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Surface Area of Pyramids[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><span style=\"color: #16a085;\"><strong>Find the total surface area of the pyramid.<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-pyramids\"><img loading=\"lazy\" class=\"alignnone wp-image-4367 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/3-33.png\" alt=\"\" width=\"200\" height=\"280\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-pyramids”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”25px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><span style=\"color: #16a085;\"><strong>Oliver is making a toybox from wood in the shape of a pyramid. Dimensions are below. How many square meters of wood are needed?<\/strong><\/span><br \/>\nRound your answer to the nearest tenth.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-pyramids\"><img loading=\"lazy\" class=\"alignnone wp-image-4369 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/4-25.png\" alt=\"\" width=\"161\" height=\"282\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-pyramids”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”25px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><span style=\"color: #16a085;\"><strong>The pendant in the shape of a pyramid have dimensions below. Find the surface area.<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-pyramids\"><img loading=\"lazy\" class=\"alignnone wp-image-4373 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/5-16.png\" alt=\"\" width=\"194\" height=\"251\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-pyramids”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”25px”][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Surface area:<\/strong> It is the sum of the areas of all the surfaces of a three-dimensional figure.<\/p>\n<p><strong>Lateral area:<\/strong> It is the surface area of the figure, excluding the area of the base(s) of a three-dimensional figure.<\/p>\n<p><strong>Regular pyramid<\/strong> \u2013 a pyramid with a base that is a regular polygon.<\/p>\n<p><strong>Slant height<\/strong> \u2013 the height of a lateral face.<\/p>\n<p><strong>Net:<\/strong> A two-dimensional shape that can be modified to form a three-dimensional shape or a solid. A 3-D shape may have different nets.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635499698510{border-radius: 10px !important;}”]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/nets-of-3-dimensional-figures\"><span style=\"color: #ed5600;\">Nets of 3 Dimensional Figures<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-prisms\"><span style=\"color: #ed5600;\">Surface Area of Prisms<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/surface-area-of-rectangular-prisms\"><span style=\"color: #ed5600;\">Surface Area of Rectangular Prisms<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cylinders\"><span style=\"color: #ed5600;\">Surface Area of Cylinders<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/measurement-perimeter\"><span style=\"color: #ed5600;\">Measurement – Perimeter<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/measurement-area\"><span style=\"color: #ed5600;\">Measurement – Area<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/area-of-a-parallelogram\"><span style=\"color: #ed5600;\">Area of a parallelogram<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/area-of-a-triangle\"><span style=\"color: #ed5600;\">Area of a triangle<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635499782218{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 10px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/volume-of-pyramids\">Volume of Pyramids<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/volume-of-prisms\">Volume of Prisms<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-spheres\">Volume of Spheres<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-cylinders\">Volume of Cylinders<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-cones\">Volume of Cones<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/volume-of-rectangular-prisms\">Volume of Rectangular Prisms<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cylinders\">Surface Area of Cylinders<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cones\">Surface Area of Cones<\/a><\/span>[\/vc_column_text][vc_row_inner 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el_class=”btninlinespacing”][vc_column_inner][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″ css=”.vc_custom_1633761494145{border-radius: 1px !important;}”][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Surface Area of Pyramids [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The surface area of a pyramid is obtained by adding the areas of its faces. A pyramid is a three-dimensional shape whose base is […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Surface Area of Pyramids | Oryx Learning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/surface-area-of-pyramids\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Surface Area of Pyramids\" \/>\n<meta property=\"og:description\" content=\"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″ css=”.vc_custom_1633761494145{border-radius: 1px !important;}”][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Surface Area of Pyramids [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The surface area of a pyramid is obtained by adding the areas of its faces. 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