[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523076-105":59,"doc-detail-523076-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","area-of-regular-polygons-geometry-worksheet","Area of Regular Polygons - Geometry Worksheet","","This geometry worksheet focuses on calculating the area of various regular polygons, including triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons. It provides a series of practice problems ranging from basic area calculations using given apothems and side lengths to advanced problems requiring the application of special right triangle properties. The document also includes critical thinking exercises that challenge students to derive perimeters from area values or evaluate the geometric feasibility of specific polygon dimensions. Designed for educational use, the material serves as an excellent resource for students to master polygon area formulas and geometric reasoning.",{"@graph":69,"@context":122},[70,84,105],{"@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-regular-polygons-geometry-worksheet/523076/",{"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-regular-polygons-geometry-worksheet/523076.png","ImageObject",300,407,{"name":92,"@type":93},"Stanley","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you find the area of a regular polygon given its apothem and side length?","Question",{"text":112,"@type":113},"The area of a regular polygon can be calculated using the apothem and the perimeter. The standard formula is Area = 1/2 * apothem * perimeter, where the perimeter is the number of sides multiplied by the length of one side.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the perimeter of a regular hexagon with an area of 54√3 units²?",{"text":117,"@type":113},"Following the calculations for regular polygons, the perimeter of such a hexagon is 36 units.",{"name":119,"@type":110,"acceptedAnswer":120},"Can a regular octagon have an area of 10 units²?",{"text":121,"@type":113},"Yes, a regular octagon can have an area of 10 square units, although the side lengths would not be integers.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},523076,1791512860,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},2336477405376,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Kuta Software-Infinite Geometry Name   \nArea of Regular Polygons Date  Period   \nFind the area of each regular polygon. Leave your answer in simplest form.  \n1)  \n2)    \n13.9  \n14.4  \n8  \n3)  \n4)  \n5)  \n6)  \n7) pentagon apothem = 7.3 side = 10.6  \n8) triangle apothem = 14 side = 28 3  \n9) 7-gonapothem = 21.8 side = 21  \n10) octagon apothem = 14.1 side = 11.7  \nUse what you know about special right triangles to find the area of each regular polygon. Leave your answer in simplest form.  \n11) 12)  \n13)  \n14)  \n15) quadrilateral 16) hexagon  \nradius = 16 2  16 3  \nside =  \n3  \nCritical thinking questions:  \n17) Find the perimeter of a regular hexagon 18) Can a regular octagon have an area  \nthat has an area of 54 3 units². of 10 units² ?  \nKuta Software-Infinite Geometry Name   \nArea of Regular Polygons Date  Period   \nFind the area of each regular polygon. Leave your answer in simplest form.  \n1)  \n3)  \n5)  \n7) pentagon apothem = 7.3 side = 10.6  \n193.45  \n2)    \n13.9  \n14.4  \n700.56  \n4)  \n95.625  \n6)  \n150 3  \n8) triangle 588 3 apothem = 14  \nside = 28 3  \n9) 7-gonapothem = 21.8 side = 21  \n1602.3  \n10) octagon apothem = 14.1 side = 11.7  \n659.88  \nUse what you know about special right triangles to find the area of each regular polygon. Leave your answer in simplest form.  \n11) 12)  \n13)  \n243 3  \n25 3  \n15) quadrilateral radius = 16 2  \n1024  \n14)  \n96 3  \n96 3  \n16) hexagon side = ~~ ~~163  \n128 3  \nCritical thinking questions:  \n17) Find the perimeter of a regular hexagon that has an area of 54 3 units².  \n36 units  \n18) Can a regular octagon have an area of 10 units² ?  \nYes, it just wouldn't have integral length sides.  \nCreate your own worksheets like this one with Infinite Geometry. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaicppHG7iUSzX","https://ap.wps.com/l/cbCaicppHG7iUSzX","pdf",33522,"English","# Area Calculation Problems\n## Standard Area Problems\n## Special Right Triangles and Area\n## Critical Thinking Questions","[{\"question\":\"How do you find the area of a regular polygon given its apothem and side length?\",\"answer\":\"The area of a regular polygon can be calculated using the apothem and the perimeter. The standard formula is Area = 1/2 * apothem * perimeter, where the perimeter is the number of sides multiplied by the length of one side.\"},{\"question\":\"What is the perimeter of a regular hexagon with an area of 54√3 units²?\",\"answer\":\"Following the calculations for regular polygons, the perimeter of such a hexagon is 36 units.\"},{\"question\":\"Can a regular octagon have an area of 10 units²?\",\"answer\":\"Yes, a regular octagon can have an area of 10 square units, although the side lengths would not be integers.\"}]","Area of Regular Polygons - Geometry Worksheet | PDF",1791426470]