Problem - 4609
The three segments marked with lengths are perpendicular to each other. Find the area of the outside square.
As shown below, the length of the diagonal will be $\sqrt{(9+3)^2+5^2}=13$ which means the side length is $\frac{13}{\sqrt{2}}$. It follows that the area is $\boxed{\frac{169}{2}}$ inch$^2$.
