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The Area of the Rectangle is 12 x 16 = 192. The two circular halves. So it is 192-36Phi
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Bunuel

In rectangle ABCD shown above, sides AB and CD pass through the centers of the two circles. If AB = 12 and AD = 16, what is the area of the shaded region?

(A) 120
(B) 156
(C) 192
(D) 192 – 36π
(E) 192 – 72π

Attachment:
2017-11-17_0947.png

We see that the area of the shaded region is the area of rectangle ABCD minus twice the area of a semicircle. In other words, the area of the shaded region is the area of rectangle ABCD minus the area of one circle.

Area of shaded region = area of ABCD - area of one circle

Area of shaded region = 12 x 16 - 6^2 x π

Area of shaded region = 192 - 36π

Answer: D
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