Question 27
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 $100a + b$.