2. Let planar vectors $\boldsymbol{a}, \boldsymbol{b}$ satisfy: $|\boldsymbol{a}|=1,|\boldsymbol{b}|=2, \boldsymbol{a} \perp \boldsymbol{b}$. Points $O, A, B$ are three points on the plane, satisfying $\overrightarrow{O A}=$ $2 \boldsymbol{a}+\boldsymbol{b}, \overrightarrow{O B}=-3 \boldsymbol{a}+2 \boldsymbol{b}$, then the area of $\triangle A O B$ is
Let $\boldsymbol{a}=(1,0), \boldsymbol{b}=(0,2)$, then $\overrightarrow{O A}=(2,2), \overrightarrow{O B}=(-3,4)$. Therefore, $S_{\triangle A O B}=\frac{1}{2}|2 \times 4+2 \times 3|=7$.