MathNet 2022-part-06 — 196 problems (EN–VI) Question 117

The area of the largest regular hexagon that can fit inside of a rectangle with side lengths $20$ and $22$ can be expressed as $a \sqrt{b}-c$, for positive integers $a$, $b$, and $c$, where $b$ is squarefree. Compute $100 a+10 b+c$.