In these four identical circles let us assume the center of the circle from left uppermost to left bottom most are a,b,c and d respectively

If we connect the center of the 4 circles we will get a

square. Each side of the square will be of length 2

Now, the area of the square would be \(2 *2 = 4\)

We are required to find the area of the shaded region hence we should

reduce the portion of the circle enclosed within the square that is

not shaded.

Since the side of the square are at 90 degrees to each other we know that there are 4 right triangles within the square enclosed in the circle.

For this we should find the area of 4 sectors that are not shaded.

The area of each sector would be

equal to the other three sector.

area of 1 sector = \(\frac{90}{360}\) * ∏ * \(r^2 = \frac{1}{4} *\) ∏ as radius = 1

for 4 sectors area would be \(\frac{1}{4} *\) ∏ \(* 4\) = ∏

Therefore, area of the shaded region =

4 - ∏option D
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