Answer
$\frac{25}{2}$
Work Step by Step
We have $\vec{AB}= 6\hat{i}-5\hat{j}$
and $\vec{AC}= 11\hat{i}-5 \hat{j}$.
Area of the triangle = $\frac{1}{2}|\vec{AB}\times\vec{AC}|$
Now, $\vec{AB}\times\vec{AC}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\6&-5&0\\11&-5&0\end{vmatrix}$$=(-30+55)\hat{k}= 25\hat{k}$.
Therefore, $|\vec{AB}\times\vec{AC}|=\sqrt {25^{2}}= 25$.
Required area=$ \frac{1}{2}\times25=\frac{25}{2}$
