2020 AMC 12A Problem 18

Quadrilateral $ABCD$ satisfies $\angle ABC = \angle ACD = 90^{\circ}, AC = 20$ , and $CD = 30$ . Diagonals $\overline{AC}$ and $\overline{BD}$ intersect at point $E$ , and $AE = 5$ . What is the area of quadrilateral $ABCD$ ?

$\textbf{(A) } 330 \qquad\textbf{(B) } 340 \qquad\textbf{(C) } 350 \qquad\textbf{(D) } 360 \qquad\textbf{(E) } 370$

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