A quadrilateral whose vertices lie on a single circle is called cyclic quadrilateral. This circle is called the circumcircle, and the vertices are known to be concyclic.<\/p>\n\n\n\n
The sum of the products of opposite sides of a cyclic quadrilateral is equal to the product of the two diagonals. The opposite angle of a cyclic quadrilateral is supplementary.<\/p>\n\n\n\n
The formula for the area of a cyclic quadrilateral is:<\/p>\n\n\n\n
\u221a(s\u2212a) (s\u2212b) (s\u2212c) (s\u2212d)<\/strong><\/p>\n\n\n\n Where \u201cs\u201d is called the semi-perimeter,<\/p>\n\n\n\n s = a + b +c + d \/ 2<\/p>\n\n\n\n Example 1<\/strong><\/p>\n\n\n\n Calculate the area of the quadrilateral when the sides of the quadrilateral are 30 m, 60 m, 70 m and 45 m.<\/p>\n\n\n\n Solution<\/strong><\/p>\n\n\n\n Given parameters are<\/p>\n\n\n\n a=30m<\/p>\n\n\n\n b = 60m<\/p>\n\n\n\n c = 70m<\/p>\n\n\n\n d = 45m<\/p>\n\n\n\n s = a + b +c + d \/ 2<\/p>\n\n\n\n s = 30+60+70+45 \/ 2<\/p>\n\n\n\n s = 102.5 m<\/p>\n\n\n\n Area of cyclic quadrilateral is given by<\/p>\n\n\n\n = \u221a (s\u2212a) (s\u2212b) (s\u2212c) (s\u2212d)<\/p>\n\n\n\n = \u221a(102.5\u221230)(102.5\u221260)(102.5\u221270)(102.5\u221245)<\/p>\n\n\n\n = 2399.60 square meter<\/p>\n\n\n\n Example 2<\/strong><\/p>\n\n\n\n Calculate the area of the quadrilateral when the sides of the quadrilateral are 35 m, 77 m, 75 m and 43 m.<\/p>\n\n\n\n Solution<\/strong><\/p>\n\n\n\n Given parameters are<\/p>\n\n\n\n a = 35 m<\/p>\n\n\n\n b = 77 m<\/p>\n\n\n\n c = 75 m<\/p>\n\n\n\n d = 43 m<\/p>\n\n\n\n s = a + b + c + d \/ 2<\/p>\n\n\n\n s = 35 + 77 + 75 + 43 \/ 2<\/p>\n\n\n\n s = 115 m<\/p>\n\n\n\n Area of cyclic quadrilateral is given by<\/p>\n\n\n\n \u221a(s\u2212a) (s\u2212b) (s\u2212c) (s\u2212d)<\/p>\n\n\n\n = \u221a (115\u221235)(115\u221277)(115\u221275)(115\u221243)<\/p>\n\n\n\n 2958.91 square meter<\/p>\n","protected":false},"excerpt":{"rendered":" A quadrilateral whose vertices lie on a single circle is called cyclic quadrilateral. This circle is called the circumcircle, and the vertices are known to be concyclic. The sum of the products of opposite sides of a cyclic quadrilateral is equal to the product of the two diagonals. The opposite angle of a cyclic quadrilateral […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[711],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3041"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=3041"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3041\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=3041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=3041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=3041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}