[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297334-105":59,"doc-detail-297334-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","84-surface-area-of-right-pyramids-and-cones","8.4 - Surface Area of Right Pyramids and Cones","","Lesson section 8.4 explains how to determine the surface area of right pyramids and cones. It presents multiple strategies, including using nets, calculating slant height with right-triangle relationships, finding areas of base shapes and triangular faces, and summing total surface area. Worked examples show square-based right pyramids, pyramid-on-prism surface area, and developing a cone surface area formula by relating the curved surface sector to circle circumference. It concludes with reflective and apply-the-math prompts.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/84-surface-area-of-right-pyramids-and-cones/297334/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/84-surface-area-of-right-pyramids-and-cones/297334.png","ImageObject",300,407,{"name":92,"@type":93},"Bill Black","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the main goal of section 8.4?","Question",{"text":113,"@type":114},"Determine the surface area of a pyramid and a cone using a variety of strategies, including nets and geometry relationships.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How can a net help find the surface area of a right pyramid?",{"text":118,"@type":114},"A net reveals all faces so you can calculate the area of each face (such as triangles and a polygon base) and add them to get the total surface area.",{"name":120,"@type":111,"acceptedAnswer":121},"How is the cone surface area formula developed?",{"text":122,"@type":114},"By relating the curved surface sector to the base circle using circle area and circumference relationships, then adding the base area to the curved-surface area.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},297334,1789743942,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144},24189269381491,"https://ap-avatar.wpscdn.com/avatar/160000cf11732dd8392?x-image-process=image/resize,m_fixed,w_180,h_180&k=1788146458752108895","8.4  \nYOU WILL NEED  \n• grid paper  \n right pyramid   \na pyramid whose base is a regular polygon and whose top vertex is directly above the centre of the base  \nSurface Area of Right Pyramids and Cones  \nGOAL  \nDetermine the surface area of a pyramid and a cone using a variety of strategies.  \nLEARN ABOUT the Math  \nYvonne is printing slogans on the side of this  right pyramid. She wants to calculate its surface area.  \n12 cm  \n10 cm  \n? How can Yvonne determine the area for slogans?  \n| EXAMPLE 1 Calculating surface area using a net and slant height |  |\n| --- | --- |\n| Yvonne’s Solution |  |\n| \u003Cbr>\u003Cbr>\u003Cbr>slant height\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr> 10 cm | \u003Cbr>?  I visualized the box’s net. It had four identical\u003Cbr> triangles for the sides and a square base.\u003Cbr>\u003Cbr> 10 cm\u003Cbr>|\n| 12 cm\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>10 cm\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>12 cm\u003Cbr>\u003Cbr>Abase 􀀂 s 2\u003Cbr>􀀂 10 􀀃 10\u003Cbr>􀀂 100 cm2\u003Cbr>\u003Cbr>5 cm\u003Cbr>Atriangle 􀀂\u003Cbr>􀀂\u003Cbr>c 2 􀀂 a 2 􀀄 b2  c 2 􀀂 122 􀀄 52 c 2 􀀂 144 􀀄 25 \u003Cbr>c 2 􀀂 169\u003Cbr>c 􀀂 1169\u003Cbr>c 􀀂 13\u003Cbr>I calculated the slant height.\u003Cbr>The height of the pyramid, a, was 12 cm. The distance, b, from the centre of the base to the side was half of 10 cm, or 5 cm. I visualized the 12 cm and 5 cm lengths as legs of a right triangle. The slant height, c, was the hypotenuse.\u003Cbr>121bh  2 􀀃 10 􀀃 13\u003Cbr>\u003Cbr>I calculated the area of the square base and of each triangular face.\u003Cbr>|  |\n| 􀀂 65 cm2 |  |\n| SApyramid 􀀂 A4 triangles 􀀄 Abase\u003Cbr>􀀂 4 􀀃 65 􀀄 100\u003Cbr>􀀂 360 cm2 | I calculated the total surface area. |\n\n448 Chapter 8 NEL  \n8.4  \nReflecting  \nA. How did Yvonne use what she already knew about the area of 2-D shapes to determine the area for slogans on the box?  \nB. How would you explain to a friend how to calculate the surface area of a pyramid?  \nAPPLY the Math  \nEXAMPLE 2 Solving a surface area problem using nets  \nJudy found a new box. It is a pyramid with six triangular faceson top ofa hexagonal prism. What is its surface area?  \nJudy’s Solution  \ns 􀀂 8.0 cm  \n10.0 cm  \n16.0 cm 6.9 cm  \n3.0 cm 8.0 cm  \nI used a net to see all the faces.  \nThere were six identical triangular faces and six identical rectangular faces. The base was a hexagon, so I divided it into two trapezoids.  \nAtrapezoid  \nAhexagon  \n1  \n􀀂 2 1base1 􀀄 base22 􀀃 6.9 1  \n􀀂 2 18.0 􀀄 16.0 2 􀀃 6.9 􀀂 82.8 cm2  \n􀀂 2 􀀃 Atrapezoid  \n􀀂 2 􀀃 82.8  \n􀀂 165.6 cm2  \nI calculated the area of one trapezoid.  \nI doubled that area to calculate the area of the base.  \n6.9 cm 16.0 cm  \nNEL Measurement 449  \nL 􀀂 10.0 cm  \nh 􀀂 3.0 cm  \ns 􀀂 8.0 cm  \nA6 triangles 􀀂 6 􀀃 sL2  \n8.0 􀀃 10.0  \n􀀂 6 􀀃  \n2  \n􀀂 240.0 cm2   \ncalculated the surface area of the six triangular faces using the base side length s and slant height L.  \ncalculated the surface area of the six rectangular faces using the base side length sand rectangle height h.  \nSA 􀀂 Abase 􀀄 Asides  \n􀀂 Ahexagon 􀀄 A6 triangles 􀀄 A6 rectangles  \n􀀂 165.6 􀀄 240.0 􀀄 144.0   \n􀀂 549.6 cm2  \ncalculated the total surface area of the box.  \n450 Chapter 8 NEL  \n8.4  \nSarah wants to calculate the surface area of this pyramid. The perimeter of its base is 80 cm.  \n24 cm  \nSarah’s Solution  \nL 􀀂 24 cm  \ns 􀀂 16 cm  \n11 cm  \nI created a net. I labelled it with the dimensions that I needed. The base side length, s, was  \n1 5  \nof 80 cm, or 16 cm, and  \nthe slant height, L, was 24 cm.  \nsL  \nA5 triangular faces 􀀂 5 􀀃 2  \n􀀂 5 􀀃  \n16 􀀃 24 2  \n􀀂 960 cm2  \nh 􀀂 11 cmb 􀀂 16 cm  \nAtriangle 􀀂  \n􀀂  \n􀀂  \nbh  \n2  \n11 􀀃 16 2  \n88 cm2  \nThere were five triangles, one for each side of the base.  \nI multiplied the area of one triangle by the number of sideson the base.  \nI divided the base into five congruent triangles. Each triangle had a base length of 16 cm and a height of 11 cm.  \nI calculated the area of one triangle.  \nEXAMPLE 3 Using reasoning to develop a formula for surface area of a pyramid  \nNEL Measurement 451  \nAbase 􀀂 5 􀀃 88  \n􀀂 440 cm2  \nSA 􀀂 Atriangular sides 􀀄 Abase  \n􀀂 960 􀀄 440  \n􀀂 1400 cm2 The pyramid has a surface area of 1400 cm2.  \nThere were five triangles, so I multiplied ","cbCaihrTvEOgfnoi","https://ap.wps.com/l/cbCaihrTvEOgfnoi","pdf",451027,"English","# Reflecting\n## Calculating pyramid surface area from 2-D area knowledge\n## Explaining how to calculate pyramid surface area\n# Apply the Math","[{\"question\":\"What is the main goal of section 8.4?\",\"answer\":\"Determine the surface area of a pyramid and a cone using a variety of strategies, including nets and geometry relationships.\"},{\"question\":\"How can a net help find the surface area of a right pyramid?\",\"answer\":\"A net reveals all faces so you can calculate the area of each face (such as triangles and a polygon base) and add them to get the total surface area.\"},{\"question\":\"How is the cone surface area formula developed?\",\"answer\":\"By relating the curved surface sector to the base circle using circle area and circumference relationships, then adding the base area to the curved-surface area.\"}]","8.4 - Surface Area of Right Pyramids and Cones | PDF",25]