Similar Pentagon Areas Part 2

Geometry Level 2

Let a pentasquish be a pentagon with the following properties:

Two non-adjacent right angles
All sides congruent

If the area of a pentasquish is \( \left(a+\dfrac{\sqrt{b}}{c} \right)s^2\), where \(s\) is the length of one of the sides, and \(a\), \(b\), and \(c\) are positive integers with \(b\) square-free, find \(a+b+c\).

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