13. Take two points on the parabola $y=2 x^{2}$ and two points on the line $x-y-2=0$, such that these four points form a square. Find the area of the square.
13. Let the line equation of two points $A, B$ on the parabola be $y=x+t$, then $|A B|=\sqrt{4 t+\frac{1}{2}},|B C|=\frac{|t+2|}{\sqrt{2}}$, from $|A B|=$ $|B C|, \sqrt{\frac{1}{2}+4 t}=\frac{|t+2|}{\sqrt{2}}, t=1$ or 3 , hence the area of the square is $\frac{9}{2}$ or $\frac{25}{2}$.