{"id":505,"date":"2019-01-15T21:01:35","date_gmt":"2019-01-16T02:01:35","guid":{"rendered":"http:\/\/josmfs.net\/?p=505"},"modified":"2024-04-15T12:52:25","modified_gmt":"2024-04-15T16:52:25","slug":"polygon-areas-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/01\/15\/polygon-areas-problem\/","title":{"rendered":"Polygon Areas Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2239\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Polygon-Areas-Fig2.jpg\" alt=\"\" width=\"250\" height=\"226\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Polygon-Areas-Fig2.jpg 400w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Polygon-Areas-Fig2-300x272.jpg 300w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/>This is another problem from <a href=\"http:\/\/www.futilitycloset.com\/\">Futility Closet<\/a>, though Futility Closet provides a \u201csolution\u201d of sorts. They provide a set of steps without explaining where they came from. So I thought I would fill in the gap. The problem is to find the area of an irregular polygon, none of whose sides cross one another, if we are given the coordinates of the vertices of the polygon.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Polygon-Areas-Prob-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/01\/Polygon-Areas-190115.pdf\">Polygon Areas Problem<\/a> for a solution.<\/p>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is another problem from Futility Closet, though Futility Closet provides a \u201csolution\u201d of sorts. They provide a set of steps without explaining where they came from. So I thought I would fill in the gap. The problem is to find the area of an irregular polygon, none of whose sides cross one another, if [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[57,16,13,31],"class_list":["post-505","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-cross-product","tag-futility-closet","tag-plane-geometry","tag-vectors"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/505","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=505"}],"version-history":[{"count":7,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/505\/revisions"}],"predecessor-version":[{"id":3934,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/505\/revisions\/3934"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=505"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=505"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}