[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-297556-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-297556-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","surface-area-of-composite-3-d-objects-lesson","Surface Area of Composite 3 D Objects - Lesson","","Learn how to determine the surface area of composite 3D objects by adding outside face areas of the component solids. The guide explains breaking a composite figure into simpler rectangular prisms, calculating outside faces for each prism, then summing results while carefully subtracting any common shared area. A second example combines a rectangular prism with a cylinder, showing which cylinder faces are already included or common and how to compute the remaining side area to reach the total surface area.",{"@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/surface-area-of-composite-3-d-objects-lesson/297556/",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/surface-area-of-composite-3-d-objects-lesson/297556.png","ImageObject",300,407,{"name":42,"@type":43},"Maya Linwood","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",13,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you find the surface area of a composite 3D object?","Question",{"text":63,"@type":64},"Compute the outside surface area of each component object, then add the areas together.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Why must shared (common) areas be treated carefully?",{"text":68,"@type":64},"The area common to different objects should not be included twice; it must be subtracted from each object’s surface area when summing.",{"name":70,"@type":61,"acceptedAnswer":71},"In Example 2, which cylinder areas are already included or not part of the composite surface area?",{"text":72,"@type":64},"The cylinder top is already included in the rectangular prism calculation, and the cylinder bottom is a common area, so neither is recalculated as part of the composite object’s surface.","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},297556,1789745744,{"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":96,"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":55},962084928432,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","9SS2.2 Determine the surface area of composite 3D objects to solve problems.  \nSurface Area of Composite 3 D Objects  \nThree dimensional (3D) composite objects are made of two or more objects put together. To calculate the surface area of a 3 D composite object, find the outside surface area of each object and then add the surface areas together.  \nExample 1  \nFind the surface area of the given composite object   mm2  \nSolution  \nStep 1  \nBreak the object into two rectangular prisms: one on the left and one on the right  \nIt could also be broken into one on top and one on the bottom.  \nStep 2  \nDetermine the surface area of the outside faces of the right prism.  \nThere are five faces front and back, top and bottom, and right side. There is no left side because it is attached to the other prism.  \nAfront and back  \nAtop and bottom  \nA  \nright side  \n= 2(lh)  \n= 2(20 x 60)  \n= 2400 mm2  \n= 2(lw)  \n= 2(60 x 10)= 1200 mm2  \n= wh  \n= 20 x 10  \n= 200 mm2  \nSAright rectangular prism = Afront and back + Atop and bottom + Aright side  \n= 2400 + 1200 + 200  \n= 3800 mm2  \nThe surface area of the outside faces of the right rectangular prism is 3800 mm2 .  \nStep 3  \nDetermine the surface are of the outside faces of the left prism.  \nThere are six faces front and back, top and bottom, left, and a partial right side  \nAfront and back  \nAtop and bottom  \nAleft side  \nA  \nright side  \n= 2(lh)  \n= 2(20 x 60)  \n= 2400 mm2  \n= 2(lw)  \n= 2(20 x 10)  \n= 400 mm2  \n= wh  \n= 60 x 10  \n= 600 mm2  \n= wh A left side of right prism = 60 x 10 200 = 400 mm2  \nSAleft rectangular prism = Afront and back + Atop and bottom + Aleft side + Aright side  \n= 2400 + 400 + 600 + 400  \n= 3800 mm2  \nThe surface area of the outside faces of the left rectangular prism is 3800 mm2 .  \nStep 4  \nFind the surface area of all the outside faces of the composite object.  \nSAcomposite figure = SAright rectangular prism + SAleft rectangular prism  \n= 3800 + 3800  \n= 7600 mm2  \nThe total surface area of the composite object is 7600 mm2 .  \nSpecial attention must be given to the area common to the different objects. Make sure it is not included in the surface area of each object and that it is subtracted from the surface area of each object.  \nComposite objects are often made up of different types of objects including a combination of rectangular prisms, triangular prisms, or cylinders.  \nExample 2  \nA composite object is illustrated in the given diagram.  \nThe surface area of the composite object, to the nearest whole number, is   cm2 .  \nSolution  \nStep 1  \nCalculate the surface area of the rectangular prism.  \nFront and Back ( 2 Equal Rectangles)  \nAfront and back = 2(l x w)  \n= 2(40 x 10)  \n= 2(400)  \n= 800 cm2  \nSides (2 equal rectangles)  \nAsides = 2(l x w)  \n= 2(25 x 10)  \n= 2(250)  \n= 500 cm2 Bottom and Top  \nAbottom = l x w  \n= 40 x 25  \n= 1000 cm2  \nBefore we calculate the area of the top let us take a bird’s eye view of it.  \nNow we could look at this shape as 2 different pieces and calculate the area of the rectangle then subtract the area of the circle…then later calculate the area of the circle and add it to the total surface area…we could use the fact that when we calculate the Total surface area of the rectangle the circle will be included and not even calculate it. EUREKA! Save use some work!  \n( Go back and look at the original Example 1… Could we have used this same idea there as well?)  \nTherefore, from our calculation before.  \nATop = ABottom = 1000 cm2 ATop and Bottom = 2000 cm2  \nSurface area for the rectangular prism is the sum of all faces.  \nSA = Afront and back + Atop and bottom + Asides  \n= 800 + 2000 + 500  \n= 3300 cm2  \nStep 2  \nCalculate the surface area of the cylinder.  \nTop of the Cylinder  \nRemember! We’ve already calculated this as it is included in the surface area of the rectangle.  \nBottom of the cylinder is a common area, not part of the surface area of the composite object. Again, no need to calculate.  \nSide of the cylinder (rectangle)  \nAsi","cbCaiejMAYnAl76e","https://ap.wps.com/l/cbCaiejMAYnAl76e","pdf",216382,"English","# 9SS2.2 Determine the Surface Area of Composite 3D Objects\n## Outside Surface Area Method\n## Example 1: Two Rectangular Prisms\n## Example 2: Rectangular Prism and Cylinder","[{\"question\":\"How do you find the surface area of a composite 3D object?\",\"answer\":\"Compute the outside surface area of each component object, then add the areas together.\"},{\"question\":\"Why must shared (common) areas be treated carefully?\",\"answer\":\"The area common to different objects should not be included twice; it must be subtracted from each object’s surface area when summing.\"},{\"question\":\"In Example 2, which cylinder areas are already included or not part of the composite surface area?\",\"answer\":\"The cylinder top is already included in the rectangular prism calculation, and the cylinder bottom is a common area, so neither is recalculated as part of the composite object’s surface.\"}]","Surface Area of Composite 3 D Objects - Lesson | PDF"]