Q15. - Algebra 2

Question

If the points $P\left(-2,3\right),Q\left(2,5\right)\text{ and }R\left(2,3\right)$ are vertices of a triangle, what is the area of the triangle?

Step-by-Step Solution

Answer

The area of the triangle is 4 units square. 

Step-1 – Apply the concept of area of right angled triangles

Area of a triangle is half into the product of its base and height. So, if b is the base and h is its height, area of triangle is calculated as.

$A=\frac{1}{2}\left(\text{base}\right)\left(\text{height}\right)$

Step-2 –Plot vertices of the triangle

Consider the provided vertices of the triangle $P\left(-2,3\right),Q\left(2,5\right)\text{ and }R\left(2,3\right)$.

Plot the points on Cartesian plane and join them

The triangle is a right angled.

Step-3 –Find the area

The area of the triangle is half times the base and height.

The base of the triangle is 4 units.

The height of the triangle is 2 units.

Therefore, the area of triangle is expressed as below.

$\begin{array}{c}A=\frac{1}{2}\left(\text{base}\right)\left(\text{height}\right)\\ =\frac{1}{2}\left(4\right)\left(2\right)\\ =4\end{array}$

Thus, the area of the triangle is 4 units square.