HMMT 2021 G2

Let $X_{0}$ be the interior of a triangle with side lengths 3,4 , and 5 . For all positive integers $n$, define $X_{n}$ to be the set of points within 1 unit of some point in $X_{n-1}$. The area of the region outside $X_{20}$ but inside $X_{21}$ can be written as $a \pi+b$, for integers $a$ and $b$. Compute $100 a+b$.