jmc

The shaded area is equal to the area of the square minus the area of the four circles. Since the side length of the square is $20$ inches, the radius of the circles is $20/4=5$ inches. The square has area $20^2=400$ square inches, and each circle has area $5^2\pi =25\pi$ square inches, so the shaded area, in square inches, is equal to $$400-4\cdot 25\pi =\boxed{400-100\pi }.$$