Question

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

Short answer

Therefore, the Area of triangle is 25 .

Step-by-step solution

Definition. 

Basically, it is equal to half of the Area of the parallelogram.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.

$\mathrm{A}=1/2\times \mathrm{b}\times \mathrm{h}$

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 triangle.

Since the area of a triangle formed by two vectors is equal to half the area of a parallelogram formed by the same vectors, we compute

$$\begin{gathered} \frac{1}{2}\left|\det \left[\begin{array}{cc}3& 8\\ 7& 2\end{array}\right]\right|=\frac{1}{2}.50 \\ \left|\mathrm{dett}\left[\begin{array}{cc}3& 8\\ 7& 2\end{array}\right]\right|=25 \end{gathered}$$

Therefore,

Area of triangle is 25 .