The perimeter of a square is the distance around the outside of the square. You can find the perimeter of any shape by adding up all of the side lengths of the shape.

However, squares are unique because all four sides of a square are equal. So, the perimeter of a square can be calculated with this formula:

\[P=4S\]

What about this?

## How to Find the Perimeter of a Square

- Find the side length of the square.
- Plug the side length into the Perimeter of a Square Formula.

## Examples

*What is the side length of the square?*

The side length of the square is \(\purple 5\, in\).

*What is the perimeter?*

When I plug \(\purple 5 \, in\) into the perimeter formula, I get…

\[P=4({\purple 5\, in})\]

Then I can simplify the expression by multiplying \(4\) by \(\purple 5\).

\[P= 20\, in\]

The perimeter is \(\purple 20\, in\).

*What is the side length of the square?*

The side length of the square is \(\green \frac{3}{5}\, ft\).

*What is the perimeter?*

When I plug \(\green \frac{3}{5}\, ft\) into the perimeter formula, I get…

\[P=4({\green \frac{3}{5}\, ft})\]

Then I can simplify the expression by multiplying the fraction by \(4\).

\[P= \frac{12}{5}\, ft\]

The perimeter is \(\green \frac{12}{5} \, ft\).

This answer is an improper fraction.

You could convert it to mixed number.

\[{\green \frac{12}{5} \, ft}= 2\frac{2}{5}\, ft\]

Or you could convert it to a decimal.

\[{\green \frac{12}{5} \, ft}=2.4\, ft\]

*What is the side length of the square?*

The side length of the square is \(\yellow 7.3\, cm\).

*What is the perimeter?*

When I plug \(\yellow 7.3 \, cm\) into the perimeter formula, I get…

\[P=4({\yellow 7.3 \, cm})\]

Then I can simplify the expression by multiplying the decimal by \(4\).

\[P= 29.2\, cm\]

The perimeter is \(\yellow 29.2\, cm\).

## Perimeter of a Rhombus

Rhombi have four sides of equal length just like squares do. So, you can use the Perimeter of a Square Formula to find the perimeter of a rhombus.

\[P=4S\]

## Why It Works

The Perimeter of a Square Formula is a special case for the general perimeter formula. It works because all the sides of a square (or rhombus) have equal lengths.

\[P=s+s+s+s\]

All four \(s\)’s are like terms so we can combine the like terms to simplify the formula.

\[P=4s\]