Hexagon

Geometry Level pending

Equilateral triangle has sides length of \(1\). Squares \(ABDE\), \(BCHI\), \(CAFG\) lie outside the triangle and on its sides. The area of hexagon \(DEFGHI\) is in the form \(a+\sqrt{b}\) where \(a\) and \(b\) are positive integers. Find \(a+b\).

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