[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-635145-105":59,"doc-detail-635145-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-a-triangle-educational-support-page","Area of a Triangle - Educational Support Page","","This educational resource provides a clear and concise explanation of the geometric formula for calculating the area of a triangle. It details the standard formula (Area = 1/2 x base x height) and explains the practical application for both right-angled triangles and general triangles. The document includes illustrative visuals to demonstrate why the formula is valid, showing the geometric relationship between a triangle and its enclosing rectangle. Designed for students, this material effectively simplifies complex mathematical concepts through visual proofs, offering a fundamental guide for mastering triangle area calculations in geometry.",{"@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-a-triangle-educational-support-page/635145/",{"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-a-triangle-educational-support-page/635145.png","ImageObject",300,407,{"name":92,"@type":93},"Aditya","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 standard formula for calculating the area of a triangle?","Question",{"text":112,"@type":113},"The area of a triangle is calculated as half of the base multiplied by the perpendicular height, expressed as 1/2 x base x height or 1/2bh.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you calculate the area of a right-angled triangle?",{"text":117,"@type":113},"For a right triangle, you simply multiply the two sides adjacent to the right angle together and then divide the result by two.",{"name":119,"@type":110,"acceptedAnswer":120},"Why is the area of a triangle equal to half the area of a rectangle?",{"text":121,"@type":113},"When a triangle is enclosed within a rectangle, it occupies exactly half of the rectangle's area, as the additional space (yellow triangles) corresponds to the same area as the sub-divided blue triangle components.","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},635145,1792980745,{"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":8,"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":81},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Name  \nAREA OF A TRIANGLE  \nDate  \nThe area of a triangle is equal to half of the base multiplied by the perpendicular height of the triangle.  \nPerpendicular height  \nArea of a triangle = ½ x b x h or ½bh.  \nIn a right triangle (left) then we simply need to multiply the 2 sides together which are adjacent to the right angle, and then halve the answer.  \nIn a triangle which is not a right triangle (right), then we need to find the perpendicular height of the triangle by dropping a vertical line down from the highest point on the triangle to the base (which needs to be horizontal) . We can then find the area by multiplying the base by this perpendicular height and halving the answer.  \nWhy does this work?  \nIf we look at the rectangle below, we can see that it has twice the area of the blue triangle inside it because the two yellow triangles are exactly the same size as the  \ntwo sub-divided blue triangles.  \nThe area of this rectangle is base x height, so the area of the triangle is half of this which is ½ x base x height.","cbCaikiMFIs1JZl4","https://ap.wps.com/l/cbCaikiMFIs1JZl4","pdf",153481,"English","# Understanding the Area of a Triangle\n## Calculating Area for Different Triangle Types\n## Geometric Proof of the Formula","[{\"question\":\"What is the standard formula for calculating the area of a triangle?\",\"answer\":\"The area of a triangle is calculated as half of the base multiplied by the perpendicular height, expressed as 1/2 x base x height or 1/2bh.\"},{\"question\":\"How do you calculate the area of a right-angled triangle?\",\"answer\":\"For a right triangle, you simply multiply the two sides adjacent to the right angle together and then divide the result by two.\"},{\"question\":\"Why is the area of a triangle equal to half the area of a rectangle?\",\"answer\":\"When a triangle is enclosed within a rectangle, it occupies exactly half of the rectangle's area, as the additional space (yellow triangles) corresponds to the same area as the sub-divided blue triangle components.\"}]","Area of a Triangle - Educational Support Page | PDF",1792675391]