[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297315-105":59,"doc-detail-297315-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","applying-our-knowledge-surface-area-and-prisms-answer-key","Applying Our Knowledge - Surface Area and Prisms - Answer Key","","Answer Key for “Applying Our Knowledge: Surface Area and Prisms” providing solutions and guidance for finding surface area of right prisms and related solids. Includes efficient formula use (2lw + 2lh + 2wh), worked dimensions for a dictionary-shaped prism, and a cube-based prism comparison. Also details a step stool extension modeled as two stacked rectangular prisms, accounting for overlaps by subtracting covered areas, with final surface area calculations in square units.",{"@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/applying-our-knowledge-surface-area-and-prisms-answer-key/297315/",{"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/applying-our-knowledge-surface-area-and-prisms-answer-key/297315.png","ImageObject",300,407,{"name":92,"@type":93},"Kyle","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","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 formula can be used efficiently to find the surface area of a right prism?","Question",{"text":113,"@type":114},"Use the efficient formula 2lw + 2lh + 2wh, which sums pairs of opposite rectangular faces.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is the dictionary’s surface area determined in the key?",{"text":118,"@type":114},"The key calculates the areas of the cover and back, then adds the areas of the spine and the book’s top and bottom, using 2(lw + lh + wh) as the efficient approach.",{"name":120,"@type":111,"acceptedAnswer":121},"How is the step stool problem solved when it is made of two rectangular prisms?",{"text":122,"@type":114},"Compute surface areas for each prism portion, then subtract the overlapping area where the top covers part of the bottom step before combining the modified totals for the final answer.","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},297315,1789743784,{"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":144},3985741905716,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Answer Key  \nApplying Our Knowledge: Surface Area and Prisms  \nDirections: solve the following 3 questions.  \n1. How does one find the surface area of a right prism?  \n2lw + 2lh + 2wh (Note: students may explain this using words or the formula)  \n2. David bought a dictionary for his English tutor as a gift. Help David find the surface area of the dictionary so that he knows how much wrapping paper to buy. Assume all sides are flat, meaning that the cover and back have no overhang. What is the surface area of the dictionary?  \nGoal: What is the surface area of the dictionary?  \nEfficient Formula: 2lw + 2lh + 2wh  \nTotal Area as a sum (Surface Area): 54 + 54 + 18 + 18 + 12 + [12 = 168 sq. in](12 = 168 sq. in).  \nSurface Area using efficient formula: 2(54) + 2(18) + 2(24) = [168 sq.in](168 sq.in).  \nGuiding Questions:  \na. What will you do first? Write a sentence to explain your thinking. *Answers could be given in a different order.  \nCover area: 6in x 9in = 54 sq. in.  \nBack cover area: 6in x 9in = 54 sq. in.  \nb. What will you do next? Write a sentence to explain your thinking.  \nLong side area spine: 9in. x 2in = 18 sq. in.  \nPage side area opposite spine: 9in. x 2in = 18 sq. in.  \nc. What will you do last? Write a sentence to explain your thinking.  \nFoot/Base of book: 6in. x 2in. = 12 sq. in.  \nHead/Top of book: 6in x 2in. = 12 sq. in.  \n2in  \n9 in  \n6 in  \n3. A. Find the surface area of the image below.  \nB. Do you notice anything about this shape that is similar or different from the shape in question 1? Share your thoughts.  \n4cm  \n4cm  \n4cm  \nA. Area of the image using a totaling strategy and using an efficient formula strategy for finding the surface area of a right prism (2lw + 2lh + 2wh) .  \nArea of bottom: 4cm x 4cm = 16 sq. cm.  \nArea of top: 4cm x 4cm = 16 sq. cm.  \nArea of front: 4cm x 4cm = 16 sq. cm.  \nArea of back: 4cm x 4cm. = 16 sq. cm.  \nArea of left side: 4cm. x 4cm. = 16 sq. cm.  \nArea of right side: 4cm. x 4cm. = 16 sq. cm.  \nTotal Area as a sum (Surface Area): 16 + 16 + 16 + 16 + 16 + 16 = 96 [sq. cm](sq. cm). Surface Area using efficient formula: 2(16) + 2(16) + 2(16) = [96 sq. cm](96 sq. cm).  \nB. Did you notice anything? Possible answers that will show depth of  \nunderstanding and mathematical flexibility with this concept: Students may notice that all lengths of all sides were the same (4cm) in the question. They may have noticed that this is a cube, not a rectangular prism or right prism. They may have noticed that the formula for the surface area of a cube can be the same as that of a right prism and they may have noticed that the formula for the surface area of a cube could be made even more efficient than that of a right prism!  \nSurface area of a cube = 6(length x width)  \n4. Find the surface area of the step stool. ( Hint: the stool is made of two rectangular prisms stacked on top of one another) .*This problem represents an extension of the original standard.  \n5 in  \n12 in 5 in  \n5 in  \n10 in  \n5 in 12in  \n10 in  \nThe students may have broken the steps into two prisms vertically or horizontally. They have enough information to successfully solve either way.  \nSurface area of a right prism efficient formula: 2( lw) + 2( lh) + 2(wh)  \nRectangle one ( horizontal bottom step) :  \nArea of base and corresponding top of base: 10 in. x 12in. = 120 sq. in. ---multiply this times 2 to get the area of the top of the bottom right prism.  \n2(120) = [240 sq. in](240 sq. in).  \nArea of long right side and long left side of bottom step:  \n12in. x 5 in. = 60 sq. in. ---multiply this times 2 to get the area of both long sides of the bottom right prism.  \n2(60) = [120 sq. in](120 sq. in).  \nArea of front and back sides of bottom step rectangular prism:  \n10 in. x 5 in. = 50 sq. in. ---multiply this times 2 to get the area of both the front and back sides of t he bottom step rectangular prism.  \n2(50) = [100 sq. in](100 sq. in).  \nAdd together all 3 totals to find the surface area of the bottom full rectangular","cbCaillMb7AO6vjG","https://ap.wps.com/l/cbCaillMb7AO6vjG","pdf",1359714,"English","# Directions\n## Question 1: Right prism surface area\n## Question 2: Dictionary surface area\n## Question 3: Image similarity and efficient strategy\n## Question 4: Step stool extension (two prisms)\n## Final combined surface area","[{\"question\":\"What formula can be used efficiently to find the surface area of a right prism?\",\"answer\":\"Use the efficient formula 2lw + 2lh + 2wh, which sums pairs of opposite rectangular faces.\"},{\"question\":\"How is the dictionary’s surface area determined in the key?\",\"answer\":\"The key calculates the areas of the cover and back, then adds the areas of the spine and the book’s top and bottom, using 2(lw + lh + wh) as the efficient approach.\"},{\"question\":\"How is the step stool problem solved when it is made of two rectangular prisms?\",\"answer\":\"Compute surface areas for each prism portion, then subtract the overlapping area where the top covers part of the bottom step before combining the modified totals for the final answer.\"}]","Applying Our Knowledge - Surface Area and Prisms - Answer Key | PDF",13]