Enclosed octagon

Geometry Level 5

ABCDABCD is a square of side length 1. E E, FF, GG and HH are the midpoints of AB AB, BCBC, CDCD and DADA, respectively. The lines FAFA, AGAG, GBGB, BHBH, HCHC, CECE, EDED and DFDF determine a convex 8-gon. By symmetry, this octagon has equal sides. If ss is the side length of the octagon, then s2 s^2 can be expressed as ab \frac {a}{b} , where aa and bb are coprime positive integers. What is the value of a+ba+b?

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