Quadrilateral A E C D satisfies \angle A B C=\angle A C D=90^{\circ}, A C=20, and C D=30. Diagonals \overline{A C} and \overline{B D} intersect at point E, and A E=5. What is the area of quadrilateral A B C D ?

**Answer Choices**

A. 330

B. 340

C. 350

D. 360

E. 370