Question

Find the area of triangle DEF with vertices D(-1,2), E(3,-2) and F(-2,-2).*

Answer 1

The area of the triangle DEF is 10.

Explanation:

Area of a Triangle:

A triangle of base B and height H (both must be perpendicular) has an area of:

`\displaystyle A=(BH)/(2)`

The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.

This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:

B=3-(-2)=3+2=5

Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.

H=2-(-2)=4

With these two values, we calculate the area:

`\displaystyle A=(5*4)/(2)=10`

The area of the triangle DEF is 10.