[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-633325-105":59,"doc-detail-633325-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-and-perimeter-of-rectangles-challenge-3","Area and Perimeter of Rectangles - Challenge 3","","This document provides a math learning exercise focused on the relationship between perimeter and area in quadrilaterals. It challenges students to construct three distinct rectangles that share the same perimeter as a given square and then calculate and compare their respective areas. The resource includes both a student worksheet and an answer key, which features diagrams and a conceptual explanation. It helps students understand that among rectangles with a fixed perimeter, the square occupies the maximum area, providing a foundational lesson in geometry and optimization principles. The clear, step-by-step nature of the tasks makes it an excellent tool for classroom practice or independent study in mathematics, encouraging analytical thinking about geometric properties and the efficiency of shapes.",{"@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-and-perimeter-of-rectangles-challenge-3/633325/",{"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-and-perimeter-of-rectangles-challenge-3/633325.png","ImageObject",300,407,{"name":92,"@type":93},"Ophelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-22",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the objective of this math challenge?","Question",{"text":112,"@type":113},"The objective is to draw three different rectangles that share the same perimeter as a specific square, calculate their areas, and determine whether a larger area is possible for that perimeter.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the main finding regarding the area of these rectangles?",{"text":117,"@type":113},"The findings indicate that the constructed rectangles all have a smaller area than the square, demonstrating that the square is the most efficient shape for maximizing area with a fixed perimeter.",{"name":119,"@type":110,"acceptedAnswer":120},"Why can't you find a rectangle with a larger area than the square for a given perimeter?",{"text":121,"@type":113},"It is impossible because, among rectangles with the same perimeter, the square provides the maximum area, making it the most efficient shape.","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},633325,1793141458,{"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":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"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":24},7971461741311,"https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826","Name Date  \nAREA & PERIMETER OF RECTANGLES CHALLENGE 3  \nDraw 3 different rectangles with the same perimeter as this square.  \nFind the areas of your rectangles. What do you notice?  \nIs it possible to find a rectangle the same perimeter as this square but a larger area? Explain your answer.  \nName Date  \nAREA & PERIMETER CHALLENGE 3 ANSWERS  \nDraw 3 different rectangles with the same perimeter as this square.  \n|  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  | Ar | ea 15 | squ | ares |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n\n|  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  | A | rea 1 | 2 squ | ares |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n\n\n|  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |\n|  | A |  |  |  |  |  |  |\n|  |  | rea 7 | squa | res |  |  |  |\n|  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |\n\nFind the areas of your rectangles. What do you notice?  \nThe rectangles all have a smaller area than the square.  \nIs it possible to find a rectangle the same perimeter as this square but a larger area?  \nExplain your answer. It is impossible to find a rectangle with the same perimeter as the square but a larger area because the square is the most efficient shape for getting the most area from a given perimeter (using straight lines) .","cbCairr6jQhniOqv","https://ap.wps.com/l/cbCairr6jQhniOqv","pdf",161049,"English","# Geometry Challenge\n## Rectangle Construction Task\n## Area Analysis and Comparison\n## Theoretical Explanation and Answer Key","[{\"question\":\"What is the objective of this math challenge?\",\"answer\":\"The objective is to draw three different rectangles that share the same perimeter as a specific square, calculate their areas, and determine whether a larger area is possible for that perimeter.\"},{\"question\":\"What is the main finding regarding the area of these rectangles?\",\"answer\":\"The findings indicate that the constructed rectangles all have a smaller area than the square, demonstrating that the square is the most efficient shape for maximizing area with a fixed perimeter.\"},{\"question\":\"Why can't you find a rectangle with a larger area than the square for a given perimeter?\",\"answer\":\"It is impossible because, among rectangles with the same perimeter, the square provides the maximum area, making it the most efficient shape.\"}]","Area and Perimeter of Rectangles - Challenge 3 | PDF",1792671978]