2. In a convex quadrilateral $A B C D$, the diagonals $A C$ and $B D$ intersect at point $O$. If $S_{\triangle O A D}=4, S_{\triangle O B C}=9$, then the minimum value of the area of the convex quadrilateral $A B C D$ is
2. 25 .

Let $S_{\triangle A O B}=x, S_{\triangle C O D}=y$. Then
$$
\frac{4}{x}=\frac{O D}{O B}=\frac{y}{9} \Rightarrow x y=36 \text {. }
$$

Thus, $x+y \geqslant 2 \sqrt{x y}=12$.
Equality holds if and only if $x=y=6$.
Therefore, $S_{\text {quadrilateral } A B C D}=4+9+x+y \geqslant 25$.
Equality holds if and only if $x=y=6$.