Problem Solving (PS) | Two semi-circles are drawn on adjacent sides of a square with side len

First we must obtain the areaof 4 semicircles intersections by:

16 (area of square) - (area of square - 2 semicircles)*2 = 16 - (16 -4π)*2 =16 - 32 - 8π = 8π-16

We just need 1 intersection, so (8π-16)/4= 2π -4

Then, in order to get the area of the shaded part we must do thefollowing:

Area of square - 2 semicircles + 1 semicircles intersection=

16 - 4π + 2π - 4 = 12 - 2π

So (B) is our answer.
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