In triangle A B C, A B=13, B C=14, and A C=15. Let D denote the midpoint of \overline{B C} and let E denote the intersection of \overline{B C} with the bisector of angle B A C. Which of the following is closest to the area of the triangle A D E ?

**Answer Choices**

A. 2

B. 2.5

C. 3

D. 3.5

E. 4