For the ellipse $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$, let F be the focus with positive $x$-coordinate and $\mathrm { F } ^ { \prime }$ be the focus with negative $x$-coordinate. A point P on this ellipse is chosen in the first quadrant such that $\angle \mathrm { FPF } ^ { \prime } = \frac { \pi } { 2 }$, and a point Q with positive $y$-coordinate is chosen on the extension of segment FP such that $\overline { \mathrm { FQ } } = 6$. Find the area of triangle $\mathrm { QF } ^ { \prime } \mathrm { F}$. [4 points]
For the ellipse $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$, let F be the focus with positive $x$-coordinate and $\mathrm { F } ^ { \prime }$ be the focus with negative $x$-coordinate. A point P on this ellipse is chosen in the first quadrant such that $\angle \mathrm { FPF } ^ { \prime } = \frac { \pi } { 2 }$, and a point Q with positive $y$-coordinate is chosen on the extension of segment FP such that $\overline { \mathrm { FQ } } = 6$. Find the area of triangle $\mathrm { QF } ^ { \prime } \mathrm { F}$. [4 points]