Answer
3 square units
Work Step by Step
We take the parallelogram as
ABCD with A=(-2,0), B=(0,3), C=(1,3), D=(-1,0)
We can translate the parallelogram to have one point at the origin (0,0) by subtracting (-2,0) from every point.
After doing the subtraction we have ;
$\textbf{A=(0,0), B=(2,3), C=(3,3), D=(1,0)}$
A parallelogram has two vectors with four vertices. The two vectors are $\textbf{u}$ and $\textbf{v}$
$\textbf{u} =AD=\begin{bmatrix}1\\0\end{bmatrix}$
$\textbf{v} =AB=\begin{bmatrix}2\\3\end{bmatrix}$
By forming a matrix $\textbf{Z}$ from the vectors $\textbf{u}$ and $\textbf{v}$
$\textbf{Z} =\left[\textbf{u},\textbf{v}\right]=\begin{bmatrix}1&2\\0&3\end{bmatrix}$
The area of a parallelogram ABCD is the absolute value of the determinant of $\textbf{Z}$
$Area\,of\,the\,parallelogram=|det\begin{bmatrix}1&2\\0&3\end{bmatrix}|=|det(3\times1-2\times0)|=3$ sq units