Answer
15 square units
Work Step by Step
We take the parallelogram as
ABCD with A=(0,-2), B=(5,-2), C=(-3,1), D=(2,1)
We can translate the parallelogram to have one point at the origin (0,0) by subtracting (0,-2) from every point.
After doing the subtraction we have ;
$\textbf{A=(0,0), B=(5,0), C=(-3,3), D=(2,3)}$
A parallelogram has two vectors with four vertices. The two vectors are $\textbf{u}$ and $\textbf{v}$
$\textbf{u} =AD=\begin{bmatrix}2\\3\end{bmatrix}$
$\textbf{v} =AB=\begin{bmatrix}5\\0\end{bmatrix}$
By forming a matrix $\textbf{Z}$ from the vectors $\textbf{u}$ and $\textbf{v}$
$\textbf{Z} =\left[\textbf{u}, \textbf{v}\right]=\begin{bmatrix}2&5\\3&0\end{bmatrix}$
The area of a parallelogram ABCD is the absolute value of the determinant of $\textbf{Z}$
$Area\,of\,the\,parallelogram=|det\begin{bmatrix}2&5\\3&0\end{bmatrix}|$
$Area\,of\,the\,parallelogram=|det(2\times0-5\times3)|=|-15|=15$ sq units
