Expected Area inside Hexagon

A regular hexagon with side length $1$ is drawn. We flip $6$ coins, with each coin corresponding to a unique midpoint of the hexagon. Then, we take all the midpoints of which their corresponding coin resulted heads, and connect them in clockwise order to create a polygon inside the hexagon. If the expected value of the area of this polygon can be expressed as $\dfrac{a\sqrt{b}}{c}$ where $a,b,c$ are positive integers, $a,c$ are coprime and $b$ is square-free, then find $a+b+c$ .

$\text{Details and Assumptions}$

A polygon with zero, one or two vertices has an area of $0$ .