That's an Ugly Looking Octagon

Geometry Level 4

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

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

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