[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297331-105":59,"doc-detail-297331-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","surface-area-of-pyramids","Surface Area of Pyramids","","A Grade 7 math lesson explains how to find the surface area of pyramids by adding the base area to the areas of all triangular faces. It emphasizes the difference between slant height and vertical height, since surface area requires slant height. Key formulas include SA = b2 + 2bℓ for square pyramids and a general pyramid form using base perimeter and slant height, with guidance for using the Pythagorean theorem. Practice and word problems apply the method.",{"@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/surface-area-of-pyramids/297331/",{"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/surface-area-of-pyramids/297331.png","ImageObject",300,407,{"name":92,"@type":93},"Rizky","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What measurements are needed to find a pyramid’s surface area?","Question",{"text":113,"@type":114},"You need the base dimensions (to compute base area) and the slant height ℓ. Vertical height H is used only to find ℓ when it is given instead of slant height.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Why can’t you use vertical height directly for surface area?",{"text":118,"@type":114},"Surface area uses the triangular faces, and each triangular face uses the slant height. Mixing up vertical height and slant height is a common mistake.",{"name":120,"@type":111,"acceptedAnswer":121},"How do you find slant height when only the vertical height and base are given?",{"text":122,"@type":114},"Form a right triangle using H, half the base (for a square base), and the slant height ℓ, then apply the Pythagorean theorem to compute ℓ.","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},297331,1789743936,{"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":24,"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":105},962085564807,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Surface Area of Pyramids  \n\n| Name:   | D | ate:   | S | core:   / 17 |\n| --- | --- | --- | --- | --- |\n\nA pyramid has one base and triangular faces that meet at the top (the apex)—and to find its surface area, you add the base area to the areas of all those triangular sides. The key measurement is the slant height: the height along a triangular face, not the straight vertical height of the whole pyramid. Mixing up those two heights is the most common mistake in pyramid problems, so label them carefully! Once you keep them separate, pyramid surface area is a straightforward calculation.  \nKey Concepts & Quick Review  \nSquare pyramid SA: SA = b2 + 4 × ~~1~~2bℓ = b2 + 2bℓ  \nAny pyramid: SA = Base area + ~~1~~2 × Pbase × ℓ (P = base perimeter, ℓ = slant height) . Slant height ℓ  vertical height H. Use: ℓ = pH2 + (b/2)2 (Pythagorean theorem) .  \nExamples  \n➀ Find the surface area of a square pyramid with base 8 cm and slant height 10 cm.  \n¬ Think It Through: For a square pyramid, total surface area is the base area plus the four triangular faces. The shortcut formula is SA = b2 +2bℓ. Substitute b = 8 and ℓ = 10: 82 +2(8)(10) = 64+160 . The base contributes 64 cm 2 , and the triangular faces together contribute 160 cm 2 , giving 224 cm 2 in total.  \n􀀑 Answer: 224 cm 2  \n➁ A square pyramid has base 12 m and vertical height 8 m. Find the slant height and surface area.¬ Think It Through: Because surface area uses slant height, find ℓ first. Draw the right triangle formed by the vertical height 8, half the base 12/2 = 6, and slant height ℓ. Then use the Pythagorean theorem: ℓ = √82 + 62 = √64 + 36 = 10 m. Now use the square pyramid formula SA = b2 + 2bℓ = 122 + 2(12)(10) = 144 + 240 = 384 m 2.  \n􀀑 Answer: ℓ = 10 m; SA = 384 m 2  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice • Progress • Succeed | Grade 7 Math · Section 8.2  \n  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n✎ Practice Problems  \nFind the surface area of each pyramid. Find ℓ first if only H is given.  \n1. Find the surface area of the square pyramid.  \nℓ = 5  \n2. Find the surface area of the square pyramid.  \n3. Find the surface area of the square pyramid.  \nℓ = 5  \nb = 6 b = 10 b = 4  \n4. Find the surface area of the square pyramid.  \nℓ = 10  \nb = 8  \n7. Find the slant height, then find the surface area.  \nb = 5  \n10. Use B  = 24 , P = 20, and ℓ = 5 to find the surface area.  \nℓ = 5  \n4  \n6  \n13. Find the slant height, then find the surface area.  \nℓ =? H = 10 .5  \nb = 20  \n5. Find the ~~slant height, then ~~find the surface area.  \nb = 9  \n8. Find the surface area of the square pyramid.  \nℓ = 25  \nb = 14  \n11. Find the slant height of the square pyramid.  \nℓ =? SA = 160  \nb = 8  \n14. Use the given base area to find the surface area.  \nℓ = 10  \nB = 36  \nb = 6  \n6. Find the ~~slant height, then ~~find the surface area.  \nb = 12  \n9. Find the surface area of the pyramid with a triangular base.  \nℓ = 8  \ns = 6  \n12. Find the surface area of the square pyramid.  \nℓ = 4  \nb = 3  \n15. Use B  = 80 , P = 36, and ℓ = 7 to find the surface area.  \n10  \nStudy Tips  \n☞ Slant height ℓ  vertical height H. Always check which one is given. Draw a right triangle cross-section to find the other.  \n☞ The lateral surface area is ~~1~~2Pℓ (","cbCaib00yVDKqe1O","https://ap.wps.com/l/cbCaib00yVDKqe1O","pdf",350006,"English","# Key Concepts & Quick Review\n## Formulas\n## Examples\n# Practice Problems\n# Study Tips\n# Word Problems","[{\"question\":\"What measurements are needed to find a pyramid’s surface area?\",\"answer\":\"You need the base dimensions (to compute base area) and the slant height ℓ. Vertical height H is used only to find ℓ when it is given instead of slant height.\"},{\"question\":\"Why can’t you use vertical height directly for surface area?\",\"answer\":\"Surface area uses the triangular faces, and each triangular face uses the slant height. Mixing up vertical height and slant height is a common mistake.\"},{\"question\":\"How do you find slant height when only the vertical height and base are given?\",\"answer\":\"Form a right triangle using H, half the base (for a square base), and the slant height ℓ, then apply the Pythagorean theorem to compute ℓ.\"}]","Surface Area of Pyramids | PDF"]