Medians to Area of Square

Median divides side into 2 equal halves. Let $BC=x$ and $AC=y$ .

Then,from question, $x^2+\left(\frac{y}{2}\right)^2=25^2$ $y^2+\left(\frac{x}{2}\right)^2=20^2$ Adding the two equations gives: $\frac{5x^2}{4}+\frac{5y^2}{4}=1025$ $\Rightarrow\space \frac{5}{4}(x^2+y^2)=1025$ $\therefore\space \text{Area of square ABEF}=(\sqrt{x^2+y^2})^2=x^2+y^2=1025\space \times\space \frac{4}{5}=\boxed{820}$