+1678 In triangle $ABC$, we have that $AB = AC,$ and $\overline{AD}$ is an altitude. Also, $E$ is a point on $\overline{AC}$ such that $\overline{BE} \perp \overline{AC}.$ If $BC = 12$ and the area of triangle $ABC$ is $180,$ what is the area of $ABDE$?
