{"id":2562,"date":"2022-01-29T09:06:50","date_gmt":"2022-01-29T14:06:50","guid":{"rendered":"https:\/\/josmfs.net\/?p=2562"},"modified":"2024-04-06T16:53:03","modified_gmt":"2024-04-06T20:53:03","slug":"octagonal-area-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/01\/29\/octagonal-area-problem\/","title":{"rendered":"Octagonal Area Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2560\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/01\/Octagonal-Area-Prob-Fig2.jpg\" alt=\"\" width=\"251\" height=\"108\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/01\/Octagonal-Area-Prob-Fig2.jpg 501w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/01\/Octagonal-Area-Prob-Fig2-300x129.jpg 300w\" sizes=\"auto, (max-width: 251px) 100vw, 251px\" \/>Here is another problem from the Polish Mathematical Olympiads published in 1960.<\/p>\n<p><strong>\u201c95<\/strong>. In a parallelogram of given area <em>S<\/em> each vertex has been connected with the mid-points of the opposite two sides.\u00a0 In this manner the parallelogram has been cut into parts, one of them being an octagon.\u00a0 Find the area of that octagon.\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Octagonal-Area-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/01\/Octagonal-Area-Problem-210811.pdf\">Octagonal Area Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is another problem from the Polish Mathematical Olympiads published in 1960. \u201c95. In a parallelogram of given area S each vertex has been connected with the mid-points of the opposite two sides.\u00a0 In this manner the parallelogram has been cut into parts, one of them being an octagon.\u00a0 Find the area of that octagon.\u201d [&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":[13,222],"class_list":["post-2562","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-plane-geometry","tag-polish-math-olympiads"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2562","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=2562"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2562\/revisions"}],"predecessor-version":[{"id":3644,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2562\/revisions\/3644"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2562"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2562"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2562"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}