4. As shown in Figure 17, $E F G H$ is an inscribed quadrilateral in square $A B C D$, and $\angle B E G$ and $\angle C F H$ are both acute angles. Given that $E G=3, F H=4$, and the area of quadrilateral $E F G H$ is 5. Find the area of square $A B C D$.
(提示: Auxiliary lines as shown in Figure 17, forming rectangle $P Q R T$. It is easy to know that $S_{\text {square } A B C D}+S_{\text {rectangle } P R R T}=2 S_{\text {quadrilateral } E F G H}$. Let $P Q=$ $x, Q R=y$, and the side length of the square be $a$. Then $x=$ $\sqrt{9-a^{2}}, y=\sqrt{16-a^{2}}$. Substituting these values, we get $a^{2}+\sqrt{9-a^{2}}$. $\sqrt{16-a^{2}}=10$. Solving this, we get $a^{2}=\frac{44}{5}$.)