8. In the Cartesian coordinate system $x O y$, let point $P$ be in the first quadrant, and points $A$ and $B$ be on $O x$ and $O y$ respectively, satisfying $P A = P B = 2$. Then the maximum value of the area of the convex quadrilateral $P A O B$ is $\qquad$
8. $2+2 \sqrt{2}$.

It is easy to see that when quadrilateral $O B P A$ is a right trapezoid, where $\angle A=45^{\circ}$ or $\angle B=45^{\circ}$, its area reaches the maximum value of $2+2 \sqrt{2}$.