Let $\mathcal{h}$ be the hyperbola with foci at $(\pm 5, 0)$ and vertices at $(\pm 3, 0),$ and let $\mathcal{c}$ be the circle with center $(0,0)$ and radius $4. $ given that $\mathcal{h}$ and $\mathcal{c}$ intersect at four points, what is the area of the quadrilateral formed by the four points?
