2007 AMC 8 Question 8

In trapezoid $ABCD,$ $\overline{AD}$ is perpendicular to $\overline{DC},$ $AD = AB = 3,$ and $DC = 6.$ In addition, $E$ is on $\overline{DC},$ and $\overline{BE}$ is parallel to $\overline{AD}.$ Find the area of $\triangle BEC.$