A geometry problem by Kaleem Kħặŋ

Geometry Level 2

Find the area of the shaded region to 2 decimal places.

(Take π = 3.142 \pi = 3.142 .)


The answer is 127.25.

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1 solution

Marta Reece
Aug 9, 2017

The four gray quarter-circles make one circle with area A g = π 9 2 A_g=\pi9^2

The four white half-circles make two circles with area A w = 2 × π ( 9 2 ) 2 A_w=2\times\pi\left(\frac92\right)^2

Total area is A g A w = π ( 81 2 × ( 9 2 ) 2 ) 127.25 A_g-A_w=\pi\left(81-2\times\left(\frac92\right)^2\right)\approx\boxed{127.25}

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