Label the shaded region as ΔABC.

The measure of each angle in a pentagon is equal to $\frac{180(5 \cdot 2)}{5} = 180^\circ$.

Therefore, the measure of $\angle BAC$ is equal to $\frac{108}{3} = 36^\circ$

Divide $\Delta ABC$ into two triangles. Use a trigonometric ratio to solve for $AD$.

$6.2$ units$^2$