If you look at one of the curves, you can see that it is the circumference of one-fourth of a circle. The center of the two circles are points B and D, therefore the radii are both 8 cm.
The perimeter of half the shape is one-fourth of a circle and there are two of the curves, so perimeter is 0.5 * C where C = 2pi*r
Perimeter = 0.5 * 2 * pi * 8 = 8pi
We can find the area of one of the non-shaded corners by taking the area of the square (8*8 = 64) and subtracting one-fourth of the circle.
64 - (0.25 * pi * 8^2) = 64 - 16pi..
There are two of these corners so multiply by 2 = 128 - 32pi
Now 64 - (128 - 32pi) = Area of shaded region.
