Question

Find the area of the parallelogram defined by$\left[\begin{array}{c}3\\ 7\end{array}\right]$and$\mathbf{\left[}\begin{array}{c}\mathbf{8}\\ \mathbf{2}\end{array}\mathbf{\right]}$.

Short answer

Therefore, the Area of parallelogram is 50.

Step-by-step solution

Definition. 

The area of a parallelogram is the number of square units inside the polygon.

The area of a parallelogram can be determined by multiplying the base and height.

For finding the area of a parallelogram, the base and height must be perpendicular. The area of a parallelogram is given by,

$\mathrm{Area}=\mathrm{b}\times \mathrm{h}$

Given. 

Given Matrix,

$\left[\begin{array}{c}3\\ 7\end{array}\right]$

And

$\left[\begin{array}{c}8\\ 2\end{array}\right]$

To find the area of the parallelogram.

Area of parallelogram formed by

$\left[\begin{array}{c}3\\ 7\end{array}\right]$

And

$\left[\begin{array}{c}8\\ 2\end{array}\right]$

Therefore,

role="math" localid="1660716122809" $$\begin{gathered} \left|det\left[\begin{array}{cc}3& 8\\ 7& 2\end{array}\right]\right|=\left|6-56\right| \\ \left|det\left[\begin{array}{cc}3& 8\\ 7& 2\end{array}\right]\right|=50 \end{gathered}$$

Area of parallelogram is 50.