Answer
6 square units
Work Step by Step
We take the parallelogram as;
$\textbf{ABCD with A=(0,0); B=(-2,4); C=(4,-5); D=(2,-1)}$
A parallelogram has 2 vectors with 4 vertices. The two vectors are $\textbf{u}$ and $\textbf{v}$
$\textbf{u} =\begin{bmatrix}2\\-1\end{bmatrix}$
$\textbf{v} =\begin{bmatrix}-2\\4\end{bmatrix}$
By forming a matrix $\textbf{Z}$ from the vectors $\textbf{u}$ and $\textbf{v}$
$\textbf{Z} =\begin{bmatrix}2&-2\\-1&4\end{bmatrix}$
The area of a parallelogram is the absolute value of the determinant of $\textbf{Z}$
$Area\,of\,the\,parallelogram\,ABCD=|det\begin{bmatrix}2&-2\\-1&4\end{bmatrix}|=|det(8-2)|=6$ sq units