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.