[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-358655-105":59,"doc-detail-358655-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","area-of-polygons-mixed-word-problems-a","Area of Polygons - Mixed Word Problems A","","Worksheets for solving mixed-area problems involving composite polygons. Students break shapes into rectangles, triangles, and trapezoids, add areas to find totals, and subtract areas for cutouts. The set includes seven school-related scenarios: a rectangular wall with a triangular roofline, an L-shaped hallway, a rectangle with a removed triangular corner, a rectangle plus a trapezoid garden section, a T-shaped stage, a rectangle with two attached triangles, and an L-shaped courtyard with a removed rectangle. An answer key provides step-by-step calculations and final areas or fencing cost.",{"@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/area-of-polygons-mixed-word-problems-a/358655/",{"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/area-of-polygons-mixed-word-problems-a/358655.png","ImageObject",300,407,{"name":92,"@type":93},"Genevieve","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-09-23",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},"How do you find the total area in these composite figure problems?","Question",{"text":113,"@type":114},"Break the figure into simpler shapes like rectangles, triangles, and trapezoids. Add the areas of the parts to get the total area.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What should you do when a shape includes a cutout or removed section?",{"text":118,"@type":114},"Subtract the area of the removed section (such as a triangular corner or an inner rectangle) from the larger base area.",{"name":120,"@type":111,"acceptedAnswer":121},"In Problem 7, how is the fencing cost calculated for the L-shaped courtyard?",{"text":122,"@type":114},"Compute the courtyard perimeter for the full L-shape, then multiply by the given cost per foot ($5 per foot).","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},358655,1790453415,{"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":19,"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":144,"read_time":52,"preview_page_count":4},1374391974585,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Name:  \n______________________________________  \nArea of Polygons—Mixed Word THE SCHOOL BUILDING  \nDirections: Solve each word problem. Show all of your work.  \nProblems (A)  \nRemember: Composite figures: break the shape into rectangles, triangles, and trapezoids. Add areas to find totalarea. Subtract areas for cutouts. Label each piece and solve step by step.  \n1. The front wall of a school includes a rectangular section 14 feet wide and 8 feet tall, plus a triangular roofline with a base of 14 feet and a height of 5 feet. What is the total area of the front wall?  \nShow your work:  \n2. A school hallway is L-shaped. The horizontal section is 16 feet by 4 feet and the vertical section is 6 feet by 8 feet. What is the total floor area?  \nShow  \nyour work:  \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)  \n3. A classroom bulletin board is a 12 ft × 6 ft rectangle with a triangular corner removed. The triangle has abase of 4 feet and a height of 6 feet. What is the remaining area?  \nShow your work:  \n4. A school garden has a rectangular section 10 ft × 8 ft and an attached trapezoidal section with parallel sides of 10 ft and 4 ft and a height of 6 ft. What is the total garden area?  \nShow your work:  \n5. A school stage is T-shaped. The top bar is 20 feet long and 5 feet wide. The vertical stem is 8 feet long and 6 feet wide. What is the total area of the stage?  \nShow your work:  \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)  \n6. A school field display is a rectangle 18 ft × 6 ft with two identical triangles added at one end. Each triangle has a base of 6 ft and a height of 4 ft. What is the total area?  \nShow  \nyour work:  \nProblem 7—Challenge  \n7. A school courtyard is a large rectangle 20 ft × 15 ft with a 6 ft × 8 ft rectangle removed from one corner.  \na. ) Draw your own diagram  \nb. ) What is the area of the courtyard?  \nc. ) If fencing costs $5 per foot and runs along the entire perimeter of the L-shape, what is the total fencing cost?  \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.) 1. ) Answer: 147 sq ft | Steps: Rect: 14 × 8 = 112 sq ft → Tri: ½ × 14 × 5 = 35 sq ft → Total: 112 + 35 = 147 sq ft  \n2.) 2. ) Answer: 112 sq ft | Steps: Horiz: 16 × 4 = 64 sq ft → Vert: 6 × 8 = 48 sq ft → Total: 64 + 48 = 112 sq ft  \n3.) 3. ) Answer: 60 sq ft | Steps: Rect: 12 × 6 = 72 sq ft → Tri removed: ½ × 4 × 6 = 12 sq ft → Remaining: 72 − 12 = 60 sq ft  \n4.) 4. ) Answer: 122 sq ft | Steps: Rect: 10 × 8 = 80 sq ft → Trap: ½ × (10 + 4) × 6 = 42 sq ft → Total: 80 + 42 = 122 sq ft  \n5.) 5. ) Answer: 148 sq ft | Steps: Top: 20 × 5 = 100 sq ft → Stem: 8 × 6 = 48 sq ft → Total: 100 + 48 = 148 sq ft  \n6.) 6. ) Answer: 132 sq ft | Steps: Rect: 18 × 6 = 108 sq ft → 2 triangles: 2 × (½ × 6 × 4) = 24 sq ft → Total: 108 + 24 = 132 sq ft  \n7.) 7 (Challenge) . )  \na.) Area = 252 sq ft  \nb.) Perimeter = 70 ft; Fencing cost = $350  \nSteps: Area: 20×15 − 6×8 = 300 − 48 = 252 sq ft  \n→ Perimeter sides: 20 + 15 + 14 + 8 + 6 + 7 = 70 ft → Cost: 70 × $5 = $350  \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)","cbCaicNn2JR8ypON","https://ap.wps.com/l/cbCaicNn2JR8ypON","pdf",3226366,"English","# Problems (A)\n## Word problem questions 1-6\n## Problem 7—Challenge\n# Answer Key","[{\"question\":\"How do you find the total area in these composite figure problems?\",\"answer\":\"Break the figure into simpler shapes like rectangles, triangles, and trapezoids. Add the areas of the parts to get the total area.\"},{\"question\":\"What should you do when a shape includes a cutout or removed section?\",\"answer\":\"Subtract the area of the removed section (such as a triangular corner or an inner rectangle) from the larger base area.\"},{\"question\":\"In Problem 7, how is the fencing cost calculated for the L-shaped courtyard?\",\"answer\":\"Compute the courtyard perimeter for the full L-shape, then multiply by the given cost per foot ($5 per foot).\"}]","Area of Polygons - Mixed Word Problems A | PDF",1790134884]