Question

What is the perimeter of a polygon with vertices at (-2,1) (-2,7) (1,11) (4,7) and (4,1)

Answer 1

28 units.

Explanation:

Consider vertices of the polygon are A(-2,1), B(-2,7), C(1,11), D(4,7) and E(4,1).

Distance formula:

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using distance formula we get

`AB=√(\left(-2-\left(-2\right)\right)^2+\left(7-1\right)^2)=6`

`BC=√(\left(1-\left(-2\right)\right)^2+\left(11-7\right)^2)=5`

`CD=√(\left(4-1\right)^2+\left(7-11\right)^2)=5`

`DE=√(\left(4-4\right)^2+\left(1-7\right)^2)=6`

`AE=√(\left(4-\left(-2\right)\right)^2+\left(1-1\right)^2)=6`

The perimeter of a polygon is

`Perimeter=AB+BC+CD+DE+AE`

`Perimeter=6+5+5+6+6`

`Perimeter=28`

Therefore, the perimeter of the polygon is 28 units.