2025 Fermat Problem 16

In the diagram, ABCD is a rectangle with area 224. Semi-circles with diameters AD and BC are drawn inside the rectangle. If the shortest distance between the semi-circles is 2, the area of the shaded region is closest to

\textbf{(A)}\ 50\quad \textbf{(B)}\ 55\quad \textbf{(C)}\ 60\quad \textbf{(D)}\ 65\quad \textbf{(E)}\ 70

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.