11.A. In the Cartesian coordinate system $x O y$, the graph of the linear function $y = kx + b (k \neq 0)$ intersects the positive half-axes of the $x$-axis and $y$-axis at points $A$ and $B$, respectively, and makes the area of $\triangle O A B$ equal to $|O A| + |O B| + 3$.
(1) Express $k$ in terms of $b$;
(2) Find the minimum value of the area of $\triangle O A B$.