AMC 12 2000 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 $ADE$?

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