Answer
$\frac{63}{2}$
Work Step by Step
Step 1. See graph, sketch the triangle with the given vertices.
Step 2. Recall the determinant formula for the area of a triangle:
$\begin{array}( \\A=\pm\frac{1}{2} \\ \\ \end{array}
\begin{vmatrix}-1 &3&1\\2&9&1\\5&-6&1 \end{vmatrix}$
Step 3. Evaluate the determinant (column3 expansion for this case)
$A=\frac{1}{2} |(1)(2(-6)-9(5))-(1)(-1(-6)-3(5))+(1)(-1(9)-3(2))|=\frac{63}{2}$
