jmc

Triangles $CHB$ and $GFB$ are similar, so we have $\frac{GF}{FB}=\frac{CH}{HB}$. Since $HB=HF+FB=18$, we see that $GF=8$. Therefore, the total area of triangles $DEA$ and $GFB$ combined is $2\cdot \frac{1}{2}(6)(8)=48$ square centimeters. The area of triangle $ABC$ is $$\frac{1}{2}(AB)(CH)=\frac{1}{2}(36)(24)=432$$ square centimeters. The area of the pentagon is the difference between these two areas, $432-48=\boxed{384}$ square centimeters.