Conic Sections · Superchallenge problem

The hyperbola $\dfrac{x^2}{9} - \dfrac{y^2}{16} = 1$ has foci $F_1 = (-5, 0)$ and $F_2 = (5, 0)$. A point $P$ on the right branch satisfies $PF_1 = 14$. Find the area of triangle $PF_1F_2$.