[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-359957-en":3,"doc-seo-359957-105":29,"detail-sidebar-cat-0-en-105":96},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":11,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":20,"preview_page_count":4},359957,1099523882182,"Alex Sinclair","https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8",4,"Exam","Surface Area - Word Problems (A) - Total Surface Area Practice","Surface Area—Word Problems (A) provides step-by-step practice for calculating total surface area of common three-dimensional figures. The problems cover rectangular prisms and open-top containers, cube-shaped boxes, triangular prisms and pyramids, and a square pyramid with given base side and slant height. A challenge problem compares two shipping box designs by computing and contrasting their surface areas, guiding students to determine which requires more material and how much.","Name:     \nSurface Area—Word Problems (A)  \nFormula Reference:  \nSA of rectangular prism = 2lw + 2lh + 2wh SA of square pyramid = b² + 4(½bl)  \nSA of triangular prism = bh + (s₁+s₂+s₃)×LSA of triangular pyramid = 4(½bl)  \nDirections: Set up and solve each problem. Show your work. Include units in your answer.  \n1.) A rectangular aquarium is 20 inches long, 10 inches wide, and 12 inches tall. It is open at the top. How many square inches of glass are needed to build the aquarium?  \n12 in  \n20 in 10 in  \n2.) A cube-shaped paper weight box has a side length of 8 cm. What is the total surface area of the box?  \n3.) A triangular prism-shaped tent has a right triangle cross-section with legs of 6 feet and 8 feet. The tent is 12 feet long. Find the total surface area of canvas needed to make the tent, including the floor.  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n4.) A trophy base is shaped like a square pyramid with a base side length of 9 cm and a slant height of 12  \ncm. Find the total surface area of the trophy base.  \n5.) A cereal box is a rectangular prism that is 30 cm tall, 20 cm wide, and 8 cm deep. How much cardboard is needed to make the cereal box?  \n6.) A rectangular-prism-shaped wooden toy chest is 3 feet long, 1.5 feet wide, and 2 feet tall. The top of the chest is left open. How many square feet of wood are needed to build the chest?  \n7.) A triangular pyramid has 4 congruent equilateral triangular faces. Each base edge is 10 m and the slant height of each face is 8.66 m. Find the total surface area.  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n8.) A rectangular swimming pool is 25 m long, 10 m wide, and 2 m deep. The pool is open at the top. How many square meters of tile are needed to cover the walls and floor of the pool?  \n9.) Challenge Problem: A company ships products in two box sizes.  \nBox A is a rectangular prism measuring 15 cm × 10 cm × 8 cm. Box B is a cube with side length 12 cm.  \na) Find the surface area of each box.  \nb) Which box requires more cardboard, and by how much?  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \nANSWER KEY  \n1.) 5 faces: 2(20×12)+2(10×12)+(20×10) = 480+240+200 920 in²  \n2.) SA = 6×8² = 6×64 384 cm²  \n3.) c=10; SA = 6×8+(6+8+10)×12 = 48+288 336 ft²  \n4.) SA = 9²+4(½×9×12) = 81+216 297 cm²  \n5.) SA = 2(20×8)+2(20×30)+2(8×30) = 320+1200+480 2000 cm²  \n6.) 5 faces: 2(3×2)+2(1 .5×2)+(3×1 .5) = 12+6+4 .5 22.5 ft²  \n7.) SA = 4(½×10×8 .66) = 4×43 .3 173.2 m²  \n8.) Floor+walls: (25×10)+2(25×2)+2(10×2) = 250+100+40 390 m²  \nChallenge:  \na) SAₐ=2(15×10)+2(15×8)+2(10×8)=300+240+160=700 cm². SAᴅ=6×12²=864 cm²  \nb) Box B uses more cardboard by 864−700 = 164 cm²  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)","cbCaikT8NmIpUeZ8","https://ap.wps.com/l/cbCaikT8NmIpUeZ8","pdf",5673674,10,1,"English","en",105,"# Problems\n## Standard Word Problems\n## Challenge Problem\n# Answer Key","[{\"question\":\"What surface area formulas are referenced for different 3D shapes?\",\"answer\":\"The sheet includes formula references for surface area of a rectangular prism, square pyramid, triangular prism, and triangular pyramid, such as SA of rectangular prism = 2lw + 2lh + 2wh and SA of square pyramid = b² + 4(½bl).\"},{\"question\":\"How should students handle “open at the top” figures in these problems?\",\"answer\":\"For containers or pools described as open at the top, the solution should exclude the top face and include only the remaining walls and floor/bottom in the total surface area.\"},{\"question\":\"What is the goal of the challenge problem comparing Box A and Box B?\",\"answer\":\"Students calculate the surface area of each box (a rectangular prism and a cube), then determine which box needs more cardboard and by how much, using the difference between their surface areas.\"}]","Surface Area - Word Problems (A) - Total Surface Area Practice | PDF",1790138322,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":90,"head_meta":92,"extra_data":94,"updated_unix":95},"surface-area-word-problems-a-total-surface-area-practice","",{"@graph":35,"@context":89},[36,52,72],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/exam/",3,{"item":51,"name":13,"@type":42,"position":11},"https://docshare.wps.com/document/surface-area-word-problems-a-total-surface-area-practice/359957/",{"url":51,"name":13,"@type":53,"image":54,"author":59,"headline":13,"publisher":61,"fileFormat":64,"inLanguage":23,"description":14,"dateModified":65,"datePublished":66,"encodingFormat":64,"isAccessibleForFree":67,"interactionStatistic":68},"DigitalDocument",{"url":55,"@type":56,"width":57,"height":58},"https://docshare.wps.com/thumbnails/surface-area-word-problems-a-total-surface-area-practice/359957.png","ImageObject",300,407,{"name":9,"@type":60},"Person",{"url":40,"name":62,"@type":63},"DocShare","Organization","application/pdf","2026-10-30","2026-09-23",true,{"@type":69,"interactionType":70,"userInteractionCount":20},"InteractionCounter",{"@type":71},"ViewAction",{"@type":73,"mainEntity":74},"FAQPage",[75,81,85],{"name":76,"@type":77,"acceptedAnswer":78},"What surface area formulas are referenced for different 3D shapes?","Question",{"text":79,"@type":80},"The sheet includes formula references for surface area of a rectangular prism, square pyramid, triangular prism, and triangular pyramid, such as SA of rectangular prism = 2lw + 2lh + 2wh and SA of square pyramid = b² + 4(½bl).","Answer",{"name":82,"@type":77,"acceptedAnswer":83},"How should students handle “open at the top” figures in these problems?",{"text":84,"@type":80},"For containers or pools described as open at the top, the solution should exclude the top face and include only the remaining walls and floor/bottom in the total surface area.",{"name":86,"@type":77,"acceptedAnswer":87},"What is the goal of the challenge problem comparing Box A and Box B?",{"text":88,"@type":80},"Students calculate the surface area of each box (a rectangular prism and a cube), then determine which box needs more cardboard and by how much, using the difference between their surface areas.","https://schema.org",{"og:url":51,"og:type":91,"og:title":13,"og:site_name":62,"og:description":14},"article",{"robots":93,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},1790435025,{"code":4,"msg":5,"data":97},[98,102,106,109,114,119,124,129,134,137,140],{"id":21,"doc_module":4,"doc_module_name":45,"category_name":99,"show_sort_weight":100,"slug":101},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":103,"show_sort_weight":104,"slug":105},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":107,"slug":108},70,"exam",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},5,"Comic",60,"comic",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},6,"Technology",50,"technology",{"id":120,"doc_module":4,"doc_module_name":45,"category_name":121,"show_sort_weight":122,"slug":123},7,"Healthcare",40,"healthcare",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":126,"show_sort_weight":127,"slug":128},8,"Research & Report",30,"research-report",{"id":130,"doc_module":4,"doc_module_name":45,"category_name":131,"show_sort_weight":132,"slug":133},9,"Religion & Spirituality",20,"religion-spirituality",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":135,"show_sort_weight":132,"slug":136},"World Cup","world-cup",{"id":20,"doc_module":4,"doc_module_name":45,"category_name":138,"show_sort_weight":20,"slug":139},"Lifestyle","lifestyle",{"id":141,"doc_module":4,"doc_module_name":45,"category_name":142,"show_sort_weight":110,"slug":143},19,"General","general"]