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