# 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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