imc

This solution is the same as Solution 1 up to the point where we find that $y=-42$. We build right triangles so we can use the Pythagorean Theorem. The triangle with hypotenuse $AB$ has legs $200$ and $2000$, while the triangle with hypotenuse $AD$ has legs $2$ and $20$. Aha! The two triangles are similar by SAS, with one triangle having side lengths $100$ times the other! Let $AD=x$. Then from our reasoning above, we have $AB=100x$. Finally, the area of the rectangle is $100x(x)=100x^2=100(20^2+2^2)=100(400+4)=100(404)=\boxed{40,400}$.