jmc

The area of the triangle formed by $0,$ $\mathbf{a},$ and $\mathbf{b}$ is half the area of the parallelogram formed by $0,$ $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{a}+\mathbf{b}.$



The area of the parallelogram formed by $0,$ $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{a}+\mathbf{b}$ is $$|(3)(2)-(-5)(1)|=11,$$so the area of the triangle is $\boxed{\frac{11}{2}}.$