Question

Find the area of the triangle below.

Short answer

Therefore, the Area of triangle is 13.

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,

$$\begin{gathered} \left[\begin{array}{c}5\\ 7\end{array}\right] \\ \left[\begin{array}{c}4\\ 3\end{array}\right] \\ \mathrm{And} \\ \left[\begin{array}{c}10\\ 1\end{array}\right] \end{gathered}$$

To find the area of the triangle.

The area of this triangle is the same as the area of a triangle formed by

$\left[\begin{array}{c}5\\ 7\end{array}\right]-\left[\begin{array}{c}4\\ 3\end{array}\right]=\left[\begin{array}{c}1\\ 4\end{array}\right]$

And

$\left[\begin{array}{c}10\\ 1\end{array}\right]-\left[\begin{array}{c}4\\ 3\end{array}\right]=\left[\begin{array}{c}6\\ -2\end{array}\right]$

Therefore,

$$\begin{gathered} \overline{)\frac{1}{2}}det\overline{)\left[\begin{array}{cc}1& 6\\ 4& -2\end{array}\right]}=\frac{1}{2}.26 \\ \overline{)\frac{1}{2}}det\overline{)\left[\begin{array}{cc}1& 6\\ 4& -2\end{array}\right]}=13 \end{gathered}$$

Area of triangle is 13.