# That's an Ugly Looking Octagon

Geometry Level 4

As shown in the diagram above, $$ABCDEFGH$$ is an inscribed octagon where $$AB=BC=CD=EF=1$$ and $$DE=FG=GH=HA=2$$.

If the area of the octagon can be expressed as $$a+b\sqrt c,$$ where $$a, b, c$$ are all integers and $$c$$ is square-free, then find the value of $$a+b+c$$.

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