Difficult# Polygon Areas: Trapezoid

GMAT-UZVXPY

A given trapezoid $ABCD$ has a line segment $AE$ that is perpendicular to side $CD$. Segment $AE$ is $4$ inches and triangle $ACE$ has area $8$ square inches.

If segment $BE$ is $ 4\sqrt{2} $inches and side $CD$ is $12$ inches, what is the area of trapezoid $ABCD$?