Evaluate the area of the shaded region, Mathematics

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Evaluate the area of the shaded region in terms of π.

223_Evaluate the area of the shaded region.png

a. 8 - 4π

b. 16 - 4π

c. 16 - 2π

d. 2π- 16

b. The area of the shaded region is same to the area of the square minus the area of the two semicircles. The area of the square is s2 or 42, which equals 16. The area of the two semicircles is same to the area of one circle. Area = πr2 or π(2)2 or 4π. Thus, the area of the shaded region is 16 - 4π. If you select a, you determine the area of the square incorrectly as 8. If you select c, you used an incorrect formula for the 1/2 πr2.


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