In coordinate space, there are two mutually perpendicular planes $\alpha$ and $\beta$. For two points $\mathrm { A }$ and $\mathrm { B }$ on plane $\alpha$, $\overline { \mathrm { AB } } = 3 \sqrt { 5 }$, and line AB is parallel to plane $\beta$. The distance between point A and plane $\beta$ is 2, and the distance between a point P on plane $\beta$ and plane $\alpha$ is 4. Find the area of triangle PAB. [4 points]