[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297319-105":59,"doc-detail-297319-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","lesson-23-area-and-volume-of-prisms-and-pyramids-learning-objectives","Lesson 23 - Area and Volume of Prisms and Pyramids - Learning Objectives","","Lesson 23 focuses on calculating surface area and volume for right prisms and regular pyramids using structured theorems and formulas. It explains that right prisms require lateral-edge perpendicularity to the base and rectangular lateral faces, then derives lateral area as L = Ph and prism volume as V = Bh. For regular pyramids, it introduces the slant-height-based surface area formula L = (1/2)Pl and volume V = (1/3)Bh, followed by worked example problems and practice assignments.",{"@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/lesson-23-area-and-volume-of-prisms-and-pyramids-learning-objectives/297319/",{"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/lesson-23-area-and-volume-of-prisms-and-pyramids-learning-objectives/297319.png","ImageObject",300,407,{"name":92,"@type":93},"Angel","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",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What formulas are used to find the lateral area and volume of a right prism?","Question",{"text":113,"@type":114},"For a right prism, lateral area is L = Ph and volume is V = Bh, where P is the base perimeter and h is the prism height, and B is the base area.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you calculate the surface area of a regular pyramid?",{"text":118,"@type":114},"For a regular pyramid, surface area is L = (1/2)(P)l, where P is the perimeter of the base and l is the slant height.",{"name":120,"@type":111,"acceptedAnswer":121},"How do you calculate the volume of a pyramid from its height and base area?",{"text":122,"@type":114},"Use V = (1/3)Bh, where h is the pyramid height and B is the area of the base.","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},297319,1789743793,{"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},687207412472,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Lesson 23: Area and Volume of Prisms and Pyramids  \nLesson Objectives:  \n• Student will apply formulas to calculate area and volume of prisms and pyramids.  \n• Student will use the properties of special right triangles to calculate measurements needed for area and volume of prisms and pyramids.  \nNow we'll look at some other shapes: prisms and pyramids.  \nThere are formulas that deal with the surface area and volume of prisms, but only right prisms. In other words, only those which are based on regular shapes, and make a right angle from the base to the matching top. \"Right prisms are prisms that have two special characteristics--all lateral edges are perpendicular to the bases, and lateral faces are rectangular. \" If one wants to know the total surface area, you can just add the area of each surface (the top and bottom, and the sides) . Often, however, the question will be asking you for the lateral area, or the area of the sides alone.  \nRight Prism Area Theorem  \nThe area L of any right prism is equal to the product of the perimeter P of abase and the height h of the prism.  \nArea (lateral area, as opposed to total area) Formula: L = Ph  \nRight Prism Volume Postulate  \nThe volume V of any right prism is the product of B (the area of the base) and the height h of the prism.  \nVolume Formula: V = Bh  \nSo for the area, the problem could look like this:  \nWhat is the area of a prism with a height of 6 and base perimeter of 24?  \nL = Ph  \nL = 24(6)  \nL = 144  \nAnd that's it!  \nA possible volume problem would be:  \nWhat is the area of the prism if the area of one base is 36 and the height is 6?  \nV = Bh  \nV = 36(6)  \nV = 216  \nAnd that's it!  \nThe only additional difficulty that might appear is that you'd have to determine the perimeter or the area of the base yourself. Remember that for squares and rectangles, the perimeter is the sum of the lengths of all the sides (or 2w + 2l), and the area is length multiplied by width.  \nRegular Pyramid Area Theorem  \nThe area L of any regular pyramid with a base that has perimeter P and with slant height l is equal to one-half the product of the perimeter and the slant height.  \nFormula: L = (1/2)(P)l  \nPyramid Volume Theorem  \nThe volume V of any pyramid with height h and a base with area B is equal to one-third the product of the height and the area of the base.  \nFormula: V = (1/3)Bh  \nA pyramid is a polyhedron with a single base and lateral faces that are all triangular. All lateral edges of a pyramid meet at a single point, or vertex. A regular pyramid is a pyramid that has a base that is a regular polygon and with lateral faces that are all congruent isosceles triangles.  \nAt any rate, the equations for area and volume are just like all the others we've done--just plug in the numbers.  \nIf a regular pyramid has a square base with a length and width of 3, and slant height of 5, and a height of 4 then what is the area of the pyramid, and what is the pyramid's volume.  \nL = (1/2)(P)l  \nL = (1/2)(12)5  \nL = 30  \nV = (1/3)Bh  \nV = (1/3)9(4)  \nV = 12  \nHere is a video.  \nVideo One  \nPractice  \nClick the link below to do some practice:  \nSolid geometry  \nGrading for this lesson:  \nTo get a 10: All answers are correct the first time, or within first revision.  \nTo get a 9: You can have 1 incorrect answer after your original submission.  \nTo get an 8: You can have 2 incorrect answers after your original submission.  \nTo get a 7: You can have 3 incorrect answers after your original submission.  \nTo get a 6: You can have 4 incorrect answers after your original submission.  \nTo get a 5: Cheating-Plagiarism-purposeful or mistaken, which will lower your final grade for the course (so be very careful when posting your work!); lack of effort, disrespect, or attitude (we are here to communicate with you if you don't understand something);  \nNote: For this class it is necessary to post the questions over each answer. Failure to do so will result in asking for a revision. No grade will be given for inco","cbCaiiidIEWDvAy9","https://ap.wps.com/l/cbCaiiidIEWDvAy9","pdf",141155,"English","# Lesson 23: Area and Volume of Prisms and Pyramids\n## Lesson Objectives\n## Right Prisms: Lateral Area and Volume\n## Regular Pyramids: Area and Volume\n## Practice and Grading","[{\"question\":\"What formulas are used to find the lateral area and volume of a right prism?\",\"answer\":\"For a right prism, lateral area is L = Ph and volume is V = Bh, where P is the base perimeter and h is the prism height, and B is the base area.\"},{\"question\":\"How do you calculate the surface area of a regular pyramid?\",\"answer\":\"For a regular pyramid, surface area is L = (1/2)(P)l, where P is the perimeter of the base and l is the slant height.\"},{\"question\":\"How do you calculate the volume of a pyramid from its height and base area?\",\"answer\":\"Use V = (1/3)Bh, where h is the pyramid height and B is the area of the base.\"}]","Lesson 23 - Area and Volume of Prisms and Pyramids - Learning Objectives | PDF",13]