9. As shown in the figure, in square $A B C D$, $E$ and $F$ are the points that trisect the diagonal $B D$. Extend $A E$ to intersect $B C$ at $G$, and extend $G F$ to intersect $A D$ at $H$. Given that $S_{\triangle D H F}=12$, then $S_{A B C D}=$ $\qquad$ _.
【Answer】 288
【Solution】Hourglass model. Connect $B H, D F: B F=D H: B G=1: 2, B G: A D=B E: E D=1: 2$, $\mathrm{G}$ is the midpoint of BC, $\mathrm{H}$ is the quartile point of $\mathrm{AD}$, $S_{\triangle A B D}=S_{\triangle D H F} \div \frac{D F}{D B} \div \frac{D H}{D A}=12 \div \frac{1}{3} \div \frac{1}{4}=144$;
$$
144 \times 2=288
$$