2025 AMC 12B Problem 12

The windshield wiper on the driver’s side of a large bus is depicted below.

Arm \overline{AB} pivots back and forth around point A, sweeping out an arc of 60^\circ, symmetric about the vertical line through A. The wiper blade \overline{CD} is attached to B at its midpoint and stays vertical as the arm moves. The arm is 3 feet long, and the wiper blade is 3.5 feet tall. What is the area of the windshield cleaned by the wiper, in square feet, to the nearest hundredth? (Assume that the windshield is a flat vertical surface.)

\textbf{(A)} 9.68 \qquad \textbf{(B)} 10.14 \qquad \textbf{(C)} 10.50 \qquad \textbf{(D)} 11.32 \qquad \textbf{(E)} 12.00

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