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