There is one circle inside a small square (whose side is 2 in that is 1/2 of the side of the square in the problem)

In my drawing when we take the area of this circle out of the area of the square we are left with 4 small shaded areas at the corners. The sum of these 4 areas is exactly the shaded area required in the problem.

Their area is: area of square of side 2 in - area of circle of diameter 2 in = 2*2 - pi*(1)^2 = 4-pi