Quadrilaterals & Polygons · Superchallenge problem

Trapezoid $ABCD$ has $\overline{AB} \parallel \overline{CD}$, $AB = 14$ and $CD = 10$. The diagonal $\overline{AC}$ bisects $\angle DAB$, and the diagonal $\overline{BD}$ bisects $\angle ABC$. Find the area of the trapezoid. Give an exact answer.