# Lengths in Polygons on the Plane

Lesson

We've looked at how to plot lines and shapes on a number plane. We've also looked at how to find lengths of horizontal, vertical and diagonal lines using the distance formula.

The Distance Formula

$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$d=(x2x1)2+(y2y1)2

We can use these different methods for measuring distance to plot polygons on a number plane, as well as to find the perimeter and area of these shapes. You just need to follow the formula for the corresponding shape.

Let's look how with some examples.

#### Worked Examples

##### Question 1

Graph the rectangle that has vertices at $\left(2.5,-1.5\right)$(2.5,1.5), $\left(2.5,2\right)$(2.5,2), $\left(-2.5,2\right)$(2.5,2) and $\left(-2.5,-1.5\right)$(2.5,1.5)

##### Question 2

Find the area of a triangle with vertices at $\left(3.5,-4\right)$(3.5,4), $\left(1.5,0\right)$(1.5,0) and $\left(0.5,-4\right)$(0.5,4)

##### Question 3

Michael is sketching a model of the area needed in his backyard for his precious rose garden on a coordinate plane with the units in feet.  If the patch needed is to be rectangular shaped with vertices at $\left(3.5,-4\right)$(3.5,4)$\left(0.5,-0.5\right)$(0.5,0.5)$\left(0.5,-4\right)$(0.5,4) and $\left(3.5,-0.5\right)$(3.5,0.5)