AMC 8 2020 Problem 18

Rectangle $ABCD$ is inscribed in a semicircle with diameter $\overline{FE},$ as shown in the figure. Let $DA=16,$ and let $FD=AE=9.$ What is the area of $ABCD?$

$\textbf{(A) }240 \textbf{(B) }248 \textbf{(C) }256 \textbf{(D) }264 \textbf{(E) }272$