The area of the dark region is found by determining the area of the larger circle and that of the smaller, and then subtracting the area of the larger from the area of the smaller.
This works out to π(16.7 in)^2 - π(12.3 in)^2, or
π(278.89 in^2 - 151.29 in^2) = 127.6π in^2 (answer)