Points $A=(0,0)$ and $B=(18,0)$ are fixed. Point $C$ moves along an ellipse defined by the equation $\frac{(x-9{)}^2}{225}+\frac{y^2}{144}=1$. As point $C$ moves around the ellipse, the centroid (center of mass) of $△ABC$ traces out a closed curve. To the nearest positive integer, what is the area of the region bounded by this curve?