2015 AMC 10B Problem 9

The shaded region below is called a shark's fin falcata, a figure studied by Leonardo da Vinci. It is bounded by the portion of the circle of radius 3 and center (0,0) that lies in the first quadrant, the portion of the circle with radius \tfrac{3}{2} and center (0,\tfrac{3}{2}) that lies in the first quadrant, and the line segment from (0,0) to (3,0). What is the area of the shark's fin falcata?

\textbf{(A) } \dfrac{4\pi}{5} \qquad\textbf{(B) } \dfrac{9\pi}{8} \qquad\textbf{(C) } \dfrac{4\pi}{3} \qquad\textbf{(D) } \dfrac{7\pi}{5} \qquad\textbf{(E) } \dfrac{3\pi}{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.