Answer
$34$
Work Step by Step
The formula for the area of a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ is:
$$\text{Area}=\pm\dfrac{1}{2}\begin{vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{vmatrix}.\tag1$$
We are given the vertices:
$$\begin{align*}
(x_1,y_1)&=(5,11)\\
(x_2,y_2)&=(9,2)\\
(x_3,y_3)&=(1,3).
\end{align*}$$
Apply formula $(1)$ to calculate the area:
$$\begin{align*}
\text{Area}&=\pm\dfrac{1}{2}\begin{vmatrix}5&11&1\\9&2&1\\1&3&1\end{vmatrix}\\
&=\pm\dfrac{1}{2}[(10+11+27)-(2+15+99)]\\
&=34.
\end{align*}$$
The area of the triangle is $34$.
