MathNet 2009-part-02 — 175 problems (EN–VI) Question 83

In a right trapezoid $ABCD$ ($AB \parallel CD$) the angle at vertex $B$ measures $75^{\circ}$. Point $H$ is the foot of the perpendicular from point $A$ to the line $BC$. If $BH = DC$ and $AD + AH = 8$, find the area of $ABCD$.