Answer
8 square units
Work Step by Step
A parallelogram has 2 vectors with 4 vertices. The two vectors are $\textbf{a}$ and $\textbf{b}$
The 4 vertices are:
W = (0,0)
X = (5,2)
Y = (6,4)
Z = (11,6)
To find the area of the parallelogram we need to find vectors $\textbf{a}$,$\textbf{b}$
WX and YZ are the vectors of adjacent sides:
$\textbf{a}= WX=\begin{bmatrix}5 \\ 2\end{bmatrix}$
$\textbf{b}= YZ=\begin{bmatrix}6 \\ 4\end{bmatrix}$
we then covert this two vectors to matrix form such that we have;
$\textbf{C} = \begin{bmatrix}5 &6\\ 2&4\end{bmatrix}$
the area of the given parallelogram = Determinant of the matrix $\textbf{C}$
area = $\textbf{det}\begin{bmatrix}5 &6\\ 2&4\end{bmatrix}=\textbf{20 - 12 = 8}$
area = 8 square units
