A Centroid Condition

In triangle $ABC$, the sides opposite angles $A, B, C$ are $a, b, c$. Given $c = 2\sqrt{5}$ and

let $O$ be the point with $\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC} = \overrightarrow{0}$, and suppose $\cos\angle CAO = \dfrac{3}{8}$. Find the area of triangle $ABC$.