Answer:
100π - 192 or 122.159....
Explanation:
In order to find the diameter we much first split the rectangle diagonally and find the hypotenuse using Pythagorean theorem.
a^2 + b^2 = c^2
16^2 + 12^2 = c^2
400 = c^2
c = 20
If the diameter of the rectangle is 20, the radius is just half of that which is 10. Then you just need to a do a basic calculation for area of a circle and then subtract out the area of the rectangle.
Area of circle = πr^2 = π(10^2) = 100π (keeping it in exact value since π is infinite)
Area of rectangle = lw = (16)(12) = 192
Area of shaded area = 100π - 192 (exact) = 122.159 (estimate)