jmc

The sides of the squares are $5,12$ and $13$ for the square with area $25,144$ and $169$, respectively. The legs of the interior triangle are $5$ and $12$, so the area is $\frac{5\times 12}{2}=\boxed{30}$ (note: the ab/2 area method only works because the converse Pythagorean theorem holds for the triple [5, 12, 13]. Therefore, we can find the solution this way because we know the triangle is right ~megaboy6679)