A disk of radius $1$ rolls all the way around the inside of a square of side length $s>4$ and sweeps out a region of area $A_1$. A second disk of radius $1$ rolls all the way around the outside of the same square and sweeps out a region of area $A_2$. If $A_1=6s-40+2\pi$ and $A_2=6s+7\pi$, and $A_2=3A_1$, the value of $s$ can be written as $a+\frac{b\pi }{c}$, where $a,b,$ and $c$ are positive integers and $b$ and $c$ are relatively prime. What is $a+b+c$?