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$