Enclosed octagon

Geometry Level 5

$ABCD$ is a square of side length 1. $E$ , $F$ , $G$ and $H$ are the midpoints of $AB$ , $BC$ , $CD$ and $DA$ , respectively. The lines $FA$ , $AG$ , $GB$ , $BH$ , $HC$ , $CE$ , $ED$ and $DF$ determine a convex 8-gon. By symmetry, this octagon has equal sides. If $s$ is the side length of the octagon, then $s^2$ can be expressed as $\frac {a}{b}$ , where $a$ and $b$ are coprime positive integers. What is the value of $a+b$ ?