Four identical circles are drawn in a square such that each

Look at the image below:The areas of regions with red dots are equal. So, we have 16 equal regions and we need the area of four of them. The area of all 16 is equal to the area of the square minus the area of four circles.

The area of the square = \(20^2 = 400\).
The area of four circles = \(4*(\pi{r^2})=4*(\pi{5^2})=100\pi\) (the diameter of each circle is 1/2 of the side, thus the radius of each circle is 1/4 of the side).

The area of 16 regions = \(400-100\pi\).
The area of shaded region (4 regions with red dots) = \(\frac{400-100\pi}{4}=100-25\pi\).

Answer: C.

Else you could simply find the area of the smaller square (1/4 of the bigger) and subtract the area of the circle. This way you'd also get the area of 4 regions with red dots.

Hope it's clear.