13. In the right figure, $ABCD$ is a parallelogram, $AM=MB$, $DN=CN$, $BE=EF=FC$, the area of quadrilateral $EFGH$ is 1, find the area of parallelogram $ABCD$.
【Answer】 $\frac{80}{9}$
【Analysis】From the kite model,
$$
\frac{B H}{H N}=\frac{S_{\triangle B M E}}{S_{\triangle N M E}}=\frac{\frac{1}{2} \times \frac{1}{3} \times \frac{1}{2}}{\frac{1}{2} \times \frac{1}{2}}=\frac{1}{3}, \frac{B G}{G N}=\frac{S_{\triangle B D F}}{S_{\triangle N D F}}=\frac{\frac{2}{3} \times \frac{1}{2}}{\frac{1}{2} \times \frac{1}{3} \times \frac{1}{2}}=\frac{4}{1}
$$

From the bird head model
$$
\begin{array}{l}
S_{\triangle B F G}=\frac{4}{5} \times \frac{2}{3} S_{\triangle B C N}=\frac{8}{15} S_{\triangle B C N}, S_{\triangle B E H}=\frac{1}{4} \times \frac{1}{3} S_{\triangle B C N}=\frac{1}{12} S_{\triangle B C N} \\
\text { Therefore, } S_{E F G H}=\left(\frac{8}{15}-\frac{1}{12}\right) S_{\triangle B C N}=\frac{27}{60} \times \frac{1}{2} \times \frac{1}{2} S_{A B C D}=\frac{9}{80} S_{A B C D}, \quad S_{A B C D}=\frac{80}{9}
\end{array}
$$