[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-634328-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-634328-en":130},{"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","right-triangle-area-harder-exercises-3","Right Triangle Area - Harder Exercises 3","","This educational document provides a set of advanced geometry practice exercises focusing on calculating the area of right-angled triangles. Learners are required to apply the Pythagorean theorem to identify missing side lengths before using the fundamental triangle area formula, which is defined as one-half times the base multiplied by the perpendicular height. The resource includes both a student worksheet featuring various problems with specific dimensions and a comprehensive answer key to facilitate self-assessment and mastery of mathematical concepts.",{"@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/right-triangle-area-harder-exercises-3/634328/",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/right-triangle-area-harder-exercises-3/634328.png","ImageObject",300,407,{"name":42,"@type":43},"Maya Linwood","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-02","2026-10-22",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the fundamental formula for calculating the area of a triangle?","Question",{"text":63,"@type":64},"The area of a triangle is calculated using the formula: one-half multiplied by the base and the perpendicular height.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What mathematical theorem is required to solve for missing sides before calculating the area?",{"text":68,"@type":64},"Pythagoras' theorem is used to determine the length of the missing side of the right-angled triangle before the area can be calculated.",{"name":70,"@type":61,"acceptedAnswer":71},"What is included in the document besides the exercise problems?",{"text":72,"@type":64},"The document includes a complete answer key that provides the calculated areas for all the geometry problems presented in the worksheet.","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},634328,1792898183,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,99,104,109,114,119,122,126],{"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":55,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":55,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":55},962084928432,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Name Date  \nRIGHT TRIANGLE AREA SHEET 3-HARDER  \nUse Pythagoras’ theorem to work out the missing side and then use this to workout the area of the following right-angle triangles. They are not drawn to scale.  \n1)  \n2)  \n4cm  \nArea =   mm 2 Area =   cm 2  \n3)  \n4) 8m  \n6cm  \nArea =   m 2  \n3.5m  \nArea =   m 2  \nArea =   cm2  \nArea =   cm2  \n2.8cm  \nHandy hint:  \nThe formula for the area of a triangle is ½ x base x (perpendicular) height  \nName Date  \nRIGHT TRIANGLE AREA SHEET 3 ANSWERS  \n1)  \n5mm  \n3cm  \n4cm  \nArea = 30 mm2 Area = 6 cm2  \n3)  \n8m  \n4)  \n6cm  \n15m 8cm  \nArea = 60 m2 Area = 24 cm2  \n5) 6)  \n3.7m  \n1.2m  5.3cm 3.5m  \n4.5cm Area = 2.1 m2 Area = 6.3 cm2  \n2.8cm","cbCaiigdkIzcd93s","https://ap.wps.com/l/cbCaiigdkIzcd93s","pdf",176033,"English","# Right Triangle Area Exercises\n## Answer Key","[{\"question\":\"What is the fundamental formula for calculating the area of a triangle?\",\"answer\":\"The area of a triangle is calculated using the formula: one-half multiplied by the base and the perpendicular height.\"},{\"question\":\"What mathematical theorem is required to solve for missing sides before calculating the area?\",\"answer\":\"Pythagoras' theorem is used to determine the length of the missing side of the right-angled triangle before the area can be calculated.\"},{\"question\":\"What is included in the document besides the exercise problems?\",\"answer\":\"The document includes a complete answer key that provides the calculated areas for all the geometry problems presented in the worksheet.\"}]","Right Triangle Area - Harder Exercises 3 | PDF",1792673631]