Answer
$\frac{11}{2}$
Work Step by Step
We have $\vec{AB}= -2\hat{i}+3\hat{j}$
and $\vec{AC}= 3\hat{i}+ \hat{j}$.
The area of the given triangle = $\frac{1}{2}|\vec{AB}\times\vec{AC}|$
Now, $\vec{AB}\times\vec{AC}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\-2&3&0\\3&1&0\end{vmatrix}$$=(-2-9)\hat{k}= -11\hat{k}$.
Therefore, $|\vec{AB}\times\vec{AC}|=\sqrt {121}= 11$.
Thus the required area is $\frac{11}{2}$
