See complete Problem 76
Area of a Circle, Square, Circular Sector, Lune. Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Monday, May 19, 2008
Elearn Geometry Problem 76
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Let the white region have an area W
ReplyDeleteThen:
pi/4 - (S1 + S2 + S3) = W -> (1)
Which is also equal to Area of circle
- Area of Blue region
Area of Circle in center of square of side 1 = pi(0.5)^2 = pi/4
Therefore W = pi/4 - S -> (2)
ie. pi/4 -(S1 + S2 + S3) = pi/4 -S
=> S1 + S2 + S3 = S
how to calc the area of S
ReplyDeleteLet the white region in the inscribed circle = S4
ReplyDeleteand side length of the square = 2x
S1 + S2 + S3 + S4 = 90/360*π*(2x)^2
= 1/4*π*4x^2
= πx^2
S + S4 = πx^2
therefore S + S4 = πx^2 = S1 + S2 + S3 + S4
thus S = S1 + S2 + S3