Let a *pentahat* be a pentagon with the following properties:

- Two adjacent right angles.
- All sides congruent.

If the area of a pentahat 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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