Problem - 2858
Let $\triangle{ABC}$ be a right triangle whose sides lengths are all integers. If $\triangle{ABC}$'s perimeter is 30, find its incircle's area.
It is easy to find out that the triangle's three sides are $(5, 12, 13)$. Then its inradius equals $$r=\frac{5+12-13}{2}=2\implies S=\boxed{4\pi}$$