Quadrilateral A B 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