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Practice questions cover triangular, cuboid-derived, and pentagonal prisms, including solving for unknown dimensions using given total surface areas or volumes, plus a real-world painting cost application.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/worksheet-82b-total-surface-areas-of-prisms-base-and-surface-area/297313/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/worksheet-82b-total-surface-areas-of-prisms-base-and-surface-area/297313.png","ImageObject",300,407,{"name":42,"@type":43},"Connor ","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-27","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",17,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How is the base of a prism defined in this worksheet?","Question",{"text":63,"@type":64},"The base is the prism’s “foundation,” equal to the bottom layer shape. The prism is formed by stacking the same base figure on top.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What is the relationship for the lateral faces area of a prism?",{"text":68,"@type":64},"The total area of all lateral faces of a prism equals the perimeter of the base multiplied by the height.",{"name":70,"@type":61,"acceptedAnswer":71},"How do you calculate the total surface area of a prism?",{"text":72,"@type":64},"Total surface area equals the total area of all lateral faces plus two times the base area.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},297313,1789743782,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":106,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":80,"read_time":144},687207022233,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Worksheet 8.2B Total Surface Areas of Prisms  \nName:   ( ) Class:   Date:   \nHow to find the base of prism?  \nThe \"base\" of the prism can be understood as the \"foundation\" of the prism, which is equal to the bottom layer of the cupcake. To complete the cupcake, we can add decoration to the layer freely.  \nHowever, to complete the prism, we cannot freely add decoration. On top of the base , We need to stack (疊) the same figure of the base. Take the triangular prism (三棱柱/三角柱體)  \nas an example  \nExample:  \nIs the base of the upper prism \"a triangle\" or \"a rectangle ''?  \nThink, if the base of the upper prism is a rectangle , can we stack the rectangles and create the prism?  \nActually, the upper prism is a horizontally placed triangular prism(三棱柱/三角柱體), and the bottom of the triangular prism is a triangle.  \nKey Points  \n1. Total area of all lateral faces ofa prism = perimeter of base 􀁵 height  \n2. Total surface area of a prism = total area of all lateral faces + 2 􀁵 base area  \nSelf learning video:  \n[https://qrgo.page.link/zRgUH](https://qrgo.page.link/zRgUH)  \n1. The figure shows a triangular prism.  \n(a) Find the total area of all its lateral faces.  \n(b) Find its total surface area.  \nSolution  \n(a) (b)  \nFind the total surface areas of the following prisms. (2 – 3)  \n7 cm  \n24 cm  \n4. In the figure, the total surface area of the cuboid is 318 cm2.  \n(a) Find the area of ABCD.  \n(b) Hence, find the value of x.  \nSolution  \n(a) (b)  \n5. In the figure, the total surface area of the prism is 276 cm2.  \n(a) Find the area of PQRS.  \n(b) Hence, find the value of x.  \nSolution  \n(a) (b)  \nA  \n6 cm  \nB 9 cm C  \nP  \nQ  \nR  \nS  \nx cm 4 cm  \n5 cm  \n12 cm  \n6. The figure shows a pentagonal prism. Its base is a regular pentagon with side length 4 cm.  \n(a) Find the total surface area of the prism.  \n(b) It is given that the cost of painting each 5 cm2 of the surface of the prism is $2.2 . How much does it cost to paint the surface of the prism?  \nSolution  \n(a) (b)  \n7. The figure shows a prism with volume 1200 cm3.  \n(a) Find the value of x.  \n(b) Find the total surface area of the prism. 15 cm Solution  \n(a) (b)  \n13 cm  \n10 cm  \n8 cm x cm  \n6 cm  \n4 cm  \narea = 27.5 cm2  \nFind the total surface areas of the following prisms. (8 – 12)  \n8.  \n8 cm   \n8 cm  \n5 cm 15 cm  \n3 cm  \n9.  \n20 cm  \n12 cm  \n10 cm  \n6 cm 6 cm  \n10.  \n15 cm  \n13 cm  13 cm  \n20 cm   15 cm  \n6 cm  \n12 cm 12 cm  \nSolution  \nSolution  \nSolution  \n11. Solution  \n12 cm  \n20 cm  \n16 cm  \n12  \ncm  \n15 cm  \n12. Solution  \n 10 cm   \n~~ ~~ 10 cm  \n 8 cm   \n14 cm     6 cm  \ncm  \n12 cm  \nFind the value of x in each of the following prisms. (13 – 14)  \n13.  \n4 cm  \n8 cm   \n4 cm  \n8 cm  \nx cm  \n12 cm   \ntotal surface area = 328 cm2  \nSolution  \n14.  \n12 cm  \ntotal surface area = 664 cm2  \nSolution  \n15. Kenny makes a cardboard pen holder in the shape of prism as shown in the figure.  \n(a) Find the total outer surface area of this pen holder.  \n(b) Kenny wants to make 5 such pen holders and paint the outer surface of the pen holders. The painting cost for each  \n4 cm2 on the outer surface is $0.05 . How much does it cost  \nto paint all the 5 pen holders?  \nSolution  \n(a)  \n(b)  \n答案：  \n1. (a) 560 cm2 (b) 728 cm2 2. 330 cm2  \n3. 688 cm2  \n4. (a) 54 cm2 (b) 7  \n5. (a) 48 cm2 (b) 6  \n6. (a) 175 cm2 (b) $77  \n7. (a) 12 (b) 700 cm2 8. 400 cm2  \n9. 1152 cm2 10. 1320 cm2 11. 1592 cm2 12. 856 cm2  \n13. 5 14. 7  \n15. (a) 440 cm2  \n12 cm  \n8 cm  \n(b) $27.5","cbCaifPYVGqq9LcV","https://ap.wps.com/l/cbCaifPYVGqq9LcV","pdf",819429,"English","# How to find the base of prism?\n# Key points\n## Lateral faces area relation\n## Total surface area formula\n# Example: triangular prism base type\n# Practice questions\n## Problems 1-6\n## Problems 7-12\n## Problems 13-14\n## Problem 15 (pen holder & painting cost)\n# Answers","[{\"question\":\"How is the base of a prism defined in this worksheet?\",\"answer\":\"The base is the prism’s “foundation,” equal to the bottom layer shape. The prism is formed by stacking the same base figure on top.\"},{\"question\":\"What is the relationship for the lateral faces area of a prism?\",\"answer\":\"The total area of all lateral faces of a prism equals the perimeter of the base multiplied by the height.\"},{\"question\":\"How do you calculate the total surface area of a prism?\",\"answer\":\"Total surface area equals the total area of all lateral faces plus two times the base area.\"}]","Worksheet 8.2B - Total Surface Areas of Prisms - Base and Surface Area | PDF",18]