# Similar Pentagon Areas Part 1

Geometry Level 3

Let a pentahat be a pentagon with the following properties:

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 $$a+b+c$$.