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 \(a+b\)?

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