Use congruence to find lengths for area

In the figure, quadrilateral $ABCD$ and quadrilateral $EFCG$ are congruent. Find the area, in $\text{cm}^2$, of quadrilateral $ABCD$.

The figure consists of a lower trapezoid $ABCD$ and a congruent quadrilateral $EFCG$ tilted above and to its right; the two quadrilaterals share vertex $C$. In trapezoid $ABCD$, the bottom side $\overline{BC}$ has length $20\ \text{cm}$. Point $H$ lies on the top side $AD$ with $\overline{AH}=8\ \text{cm}$, and the right side $\overline{DC}=6\ \text{cm}$. In the upper quadrilateral $EFCG$, side $\overline{EF}=9\ \text{cm}$. Quadrilateral $HGCD$ is a square.