tag:blogger.com,1999:blog-6933544261975483399.post6511195752161844389..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Elearn Geometry Problem 76Antonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-6933544261975483399.post-4993423981164171362018-11-25T22:19:57.892-08:002018-11-25T22:19:57.892-08:00Let the white region in the inscribed circle = S4
...Let the white region in the inscribed circle = S4<br />and side length of the square = 2x<br /><br /> S1 + S2 + S3 + S4 = 90/360*π*(2x)^2<br /> = 1/4*π*4x^2<br /> = πx^2<br /> S + S4 = πx^2<br />therefore S + S4 = πx^2 = S1 + S2 + S3 + S4<br /> thus S = S1 + S2 + S3 Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-69426413039219655782017-04-22T19:13:39.137-07:002017-04-22T19:13:39.137-07:00how to calc the area of Show to calc the area of SAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-36111859041253172882008-06-18T13:22:00.000-07:002008-06-18T13:22:00.000-07:00Let the white region have an area WThen:pi/4 - (S1...Let the white region have an area W<BR/>Then:<BR/><BR/>pi/4 - (S1 + S2 + S3) = W -> (1)<BR/><BR/>Which is also equal to Area of circle <BR/>- Area of Blue region<BR/> <BR/>Area of Circle in center of square of side 1 = pi(0.5)^2 = pi/4<BR/><BR/>Therefore W = pi/4 - S -> (2)<BR/><BR/>ie. pi/4 -(S1 + S2 + S3) = pi/4 -S<BR/><BR/> => S1 + S2 + S3 = SAnonymousnoreply@blogger.com