13. As shown in Figure 4, the area of isosceles right $\triangle ABC$ is $98$, and $D$ is a point on the hypotenuse $BC$ such that $BD: DC = 2: 5$. Then the area of the square $ADEF$ with side $AD$ is $\qquad$
13.116.

Draw $D G \perp A B, D H \perp A C$, with the feet of the perpendiculars at $G$ and $H$ respectively. It is easy to see that $A B=A C=14$.
Also, $B D: D C=G D: H D=2: 5$, so $D G=4, D H=10$. Therefore, $A D=\sqrt{4^{2}+10^{2}}$. Hence, $S_{\text {square ADEF }}=116$.