# ## Perimeter Formulas

Perimeter formulas can be used to calculate the perimeter any type of shape. However, it is not very helpful to memorize all the perimeter formulas because every type of shape has a different one and there are hundreds of types of shapes.

The best thing to do is to memorize the perimeter formulas for a few basic shapes and then learn how to create your own perimeter formulas for more complex shapes.

## Perimeter Formulas for Basic Shapes

$P=a+b+c$

$P=2\pi r$

$P=2L+2W$

$P=4s$

## How to Create Perimeter Formulas

1. Label all of the sides of the shape $$a$$, $$b$$, $$c$$, $$d$$, etc.
2. Identify which side lengths you know and write a perimeter formula $$P=a+b+c+d+…$$.
3. Find the missing side lengths.
4. Plug all the side lengths into your formula to find the perimeter.

### Examples

#### Perimeter of a Trapezoid Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec ullamcorper mattis, pulvinar dapibus leo.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec ullamcorper mattis, pulvinar dapibus leo.

#### Perimeter of a Pentagon Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec ullamcorper mattis, pulvinar dapibus leo.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec ullamcorper mattis, pulvinar dapibus leo.

## How to Find Missing Side Lengths

If one of your missing sides is parallel to a known side and they are connected with perpendicular lines, you can deduce what the missing side lengths are.

For example, in this diagram, the red and yellow sides are parallel to the green side and they are connected at their end points with perpendicular lines, so $${\red ?}+{\yellow ?}={\green ?}$$.

If one of your missing sides is slanted or part of a right triangle, you can use the Pythagorean Theorem to find the missing side.

If one of your missing sides is curved and part of a circle, you can use the arc length formula to find the length of the partial circumference.

If you are given an advanced problem without many side lengths but you know some of the angles of the shape, you can use trigonometry to find the missing side lengths.