Chapter 13.1, Problem 13PSB

To determine

To find: The area of a triangle with vertices $\left(-2,0\right)$ , $\left(4,0\right)$ , and $\left(2,3\right)$ .

Answer to Problem 13PSB

The area of the triangle is $9$ square units.

Explanation of Solution

Given:

The vertices are $\left(-2,0\right)$ , $\left(4,0\right)$ , and $\left(2,3\right)$ .

Calculation:

The base of the triangle lies along the $x$ axis so its length will be equal to $4-\left(-2\right)=6$ .

The height of the triangle lies along the $y$ axis so its length will be equal to $3-0=3$ .

Find the area of the triangle as follows.

  $\begin{array}{c}A=\frac{1}{2}\times \text{base}\times \text{height}\\ \text{=}\frac{1}{2}\left(6\right)\left(3\right)\\ =9\end{array}$

Therefore, the area of the triangle is $9$ square units.