2000 AMC 12 Problem 19

In triangle ABC, AB = 13, BC = 14, AC = 15. Let D denote the midpoint of \overline{BC} and let E denote the intersection of \overline{BC} with the bisector of angle BAC. Which of the following is closest to the area of the triangle ADE?

\textbf {(A)}\ 2 \qquad \textbf {(B)}\ 2.5 \qquad \textbf {(C)}\ 3 \qquad \textbf {(D)}\ 3.5 \qquad \textbf {(E)}\ 4

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.