3. In the Cartesian coordinate system $x O y$, the equation of ellipse $C$ is $\frac{x^{2}}{9}+\frac{y^{2}}{10}=1, F, A$ are the upper focus and the right vertex of ellipse $C$, respectively. If $P$ is a moving point on ellipse $C$ located in the first quadrant, then the maximum value of the area of quadrilateral $O A P F$ is $\qquad$
3. $\frac{3 \sqrt{11}}{2}$.

It is known that, $A(3,0), F(0,1)$.
Let $P(3 \cos \theta, \sqrt{10} \sin \theta), \theta \in\left(0, \frac{\pi}{2}\right)$.
Then $S_{\text {quadrilateral } O A P F}=S_{\triangle O A P}+S_{\triangle O F P}$ $=\frac{1}{2} \times 3 \sqrt{10} \sin \theta+\frac{1}{2} \times 1 \times 3 \cos \theta$ $=\frac{3}{2}(\sqrt{10} \cos \theta+\sin \theta)=\frac{3 \sqrt{11}}{2} \sin (\theta+\varphi)$, where, $\varphi=\arctan \frac{\sqrt{10}}{10}$.

When $\theta=\arctan \sqrt{10}$, the maximum area of quadrilateral $O A P F$ is $\frac{3 \sqrt{11}}{2}$.