Ratio between areas

Geometry Level 3

Consider a pentagon and an hexagon, both with side \(L\). Let \(A\) be the area of the pentagon, and \(B\) the area of the hexagon. If the ratio \(A:B\) can be expressed as \(\frac{\sqrt{a+b \sqrt{c}}}{d}\), then find \(a+b+c+d\).

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