[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-434702-105":59,"doc-detail-434702-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","amc-8-handout-2013-2020-problems","AMC 8 Handout - 2013-2020 Problems","","Set of AMC 8 contest problems spanning 2013 through 2020, each asking for geometric quantities such as areas, radii, probabilities, ratios, and covered fractions. Problems include rectangle and rhombus area calculations using side or diagonal information, circle configurations with shaded-region area, triangle construction from polygon vertices, and semicircle inscriptions in right or isosceles triangles. Also featured are trapezoid area derivations from equal-area shapes, region area between a rectangle and multiple circles, and grid-based coverage from plotted triangles.",{"@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/amc-8-handout-2013-2020-problems/434702/",{"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/amc-8-handout-2013-2020-problems/434702.png","ImageObject",300,407,{"name":92,"@type":93},"Grenda","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-12","2026-09-29",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What kinds of questions are included in this handout?","Question",{"text":112,"@type":113},"The handout contains AMC 8 geometry-focused problems that ask for areas, radii, ratios, probabilities, and fractions of a grid covered by a triangle.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which years and problem numbers are represented?",{"text":117,"@type":113},"It includes problems from AMC 8 years 2013, 2014, 2015, 2016, 2017, 2018, 2019, and 2020, with listed problem numbers such as 18 (2020), 4 (2019), 15/20/22/23 (2018), 16/22 (2017), 25/2 (2016), 19/25 (2015), 14/20 (2014), and 23 (2013).",{"name":119,"@type":110,"acceptedAnswer":120},"Do any problems involve probability or circle and semicircle geometry?",{"text":121,"@type":113},"Yes. One problem (AMC 8 2018, Problem 23) is explicitly a probability problem using vertices of a regular octagon. Several others involve circle or semicircle configurations, such as shaded-region area and the radius of an inscribed semicircle.","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},434702,1790838853,{"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":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"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":144},7971474921005,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","AMC 8, 2020, Problem 18  \nThree identical rectangles are put together to form rectangle  , as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5  \nfeet, what is the area in square feet of rectangle  ?  \nAMC 8, 2019, Problem 4  \nQuadrilateral  is a rhombus with perimeter  meters. The length of diagonal   \nis  meters. What is the area in square meters of rhombus ?  \nAMC 8, 2018, Problem 15  \nIn the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller circles have a combined area of  square unit, then what is the area of the shaded region, in square units?  \nAMC 8, 2018, Problem 20  \nIn  a point  is on  with  and  Point  is on  so that  \n and point  is on  so that  What is the ratio of the area of  \n to the area of   \nAMC 8, 2018, Problem 22  \nPoint  is the midpoint of side  in square  and  meets diagonal  at  The area of quadrilateral  is  What is the area of   \nAMC 8, 2018, Problem 23 (Also a probability problem!)  \nFrom a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also aside of the octagon?  \nAMC 8, 2017, Problem 16  \nIn the figure below, choose point  on  so that  and  have equal  \nperimeters. What is the area of ?  \nAMC 8, 2017, Problem 22  \nIn the right triangle  ,  ,  , and angle  is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle?  \nAMC 8, 2016, Problem 25  \nA semicircle is inscribed in an isosceles triangle with base  and height  so that the diameter of the semicircle is contained in the base of the triangle as shown. What is the radius of the semicircle?  \nAMC 8, 2016, Problem 2  \nIn rectangle  ,  and  . Point  is the midpoint of  . What is  \nthe area of ?  \nAMC 8, 2015, Problem 19  \nA triangle with vertices as  ,  , and  is p lotted on a  grid. What fraction of the grid is covered by the triangle?  \nAMC 8, 2015, Problem 25  \nOne-inch squares are cut from the corners of t his 5-inch square. What is the area in square inches of the largest square that can be fitted into the remaining space?  \nAMC 8, 2014, Problem 14  \nRectangle  and right triangle  have the same area. They are joined to form a  \ntrapezoid, as shown. What is ?  \nAMC 8, 2014, Problem 20  \nRectangle  has sides  and  . A circle of radius  is centered at  , a circle of radius  is centered at  , and a circle of radius  is centered at  . Which of the following is closest to the area of the region inside the rectangle but outside all three circles?  \nAMC 8, 2013, Problem 23  \nAngle  of  is a right angle. The sides of  are the diameters of semicircles as shown. The area of the semicircle on  equals  , and the arc of the semicircle on  has length  . What is the radius of the semicircle on ?","cbCaijDZmlm3BGpe","https://ap.wps.com/l/cbCaijDZmlm3BGpe","pdf",235625,"English","# AMC 8 2020\n## Problem 18\n# AMC 8 2019\n## Problem 4\n# AMC 8 2018\n## Problem 15\n## Problem 20\n## Problem 22\n## Problem 23\n# AMC 8 2017\n## Problem 16\n## Problem 22\n# AMC 8 2016\n## Problem 25\n## Problem 2\n# AMC 8 2015\n## Problem 19\n## Problem 25\n# AMC 8 2014\n## Problem 14\n## Problem 20\n# AMC 8 2013\n## Problem 23","[{\"question\":\"What kinds of questions are included in this handout?\",\"answer\":\"The handout contains AMC 8 geometry-focused problems that ask for areas, radii, ratios, probabilities, and fractions of a grid covered by a triangle.\"},{\"question\":\"Which years and problem numbers are represented?\",\"answer\":\"It includes problems from AMC 8 years 2013, 2014, 2015, 2016, 2017, 2018, 2019, and 2020, with listed problem numbers such as 18 (2020), 4 (2019), 15/20/22/23 (2018), 16/22 (2017), 25/2 (2016), 19/25 (2015), 14/20 (2014), and 23 (2013).\"},{\"question\":\"Do any problems involve probability or circle and semicircle geometry?\",\"answer\":\"Yes. One problem (AMC 8 2018, Problem 23) is explicitly a probability problem using vertices of a regular octagon. Several others involve circle or semicircle configurations, such as shaded-region area and the radius of an inscribed semicircle.\"}]","AMC 8 Handout - 2013-2020 Problems | PDF",1790670282,18]