**Introduction**

In this lesson, you will review how to find the perimeter of a rectangle and a square.

### Real World Application

It is important to understand the difference between a right angle, which is 90 degrees, and any other angle. As shown above, the first angle is made of perpendicular lines and is 90 degrees, which makes it a right angle. The two other angles are not made of perpendicular lines, and therefore are not right angles.

This video illustrates the lesson material below. Watching the video is optional.

**What is Perimeter?**

Here are some definitions to help you with this lesson:

**Perimeter:**The sum of the lengths of all sides of a shape.**Rectangle:**A four-sided shape whose opposite sides are the same length and all the corners form right angles. (In Figure 1, the first shape is a rectangle, and the other two are not.)

Figure 1

**Square:**A four-sided rectangle where all sides are the same length and all the corners form right angles.

Perimeter is the sum of the lengths of all sides of a shape. For rectangles and squares, you can simplify this because some of the side have the same length.

**Example 1: Perimeter of a Rectangle**

\begin{align*}P &= l + l + w + w \\P &=2l + 2w &\color{red}\small\text{Combining like terms}\\\end{align*}

**Example 2: Perimeter of a Square**

\begin{align*}P &= w + w + w + w \\P &= 4w &\color{red}\small\text{Combining like terms}\\\end{align*}

Note: P = Perimeter, l = length, and w = width

**Example 3: Solving for Perimeter**

A rectangle is 100 centimeters by 140 centimeters. What is the perimeter of the rectangle?

Figure 2

Figure 2 shows a rectangle with a width of 100 centimeters and length of 140 centimeters. The formulas for finding the perimeter of this rectangle are \(P = l + l + w +w \) or \(P = 2l + 2w\).

Below shows what the perimeter formulas look like using the two different methods:

\begin{align*}P &= l + l + w + w &\color{red}\small\text{First Formula} \\P &= 140 + 140 + 100 + 100 &\color{red}\small\text{Substitute given sides}\\P &= 480cm &\color{red}\small\text{Add}\\\end{align*}

Or

\begin{align*}P &= 2l + 2w &\color{red}\small\text{Second Formula} \\P &= 2(140) + 2(100) &\color{red}\small\text{Substitute given sides}\\P &= 280 + 200&\color{red}\small\text{Multiply}\\P &= 480cm &\color{red}\small\text{Add}\\\end{align*}

**Example 4: Solving for Perimeter**

A square is a special kind of rectangle where all of the sides have the same length.

A field is 300 feet by 300 feet. How much fence is needed to surround this field?

Figure 3

First, decide length and width: all sides are 300 feet. Because the length is equal to the width, you only have to use one or the other in the equation:

\begin{align*} Perimeter = w+w+w+w \end{align*}

Since the figure is a square, you know that \(l=w\), so the perimeter for any square is:

\begin{align*} Perimeter =4w\end{align*}

You can use one of two methods:

\begin{align*}P &= w + w + w + w &\color{red}\small\text{First Formula}\\P &=300 + 300 + 300 + 300 &\color{red}\small\text{Substitute given sides}\\P &= 1200ft &\color{red}\small\text{Add}\\\end{align*}

Or

\begin{align*}P &= 4w &\color{red}\small\text{Second Formula}\\P &= 4(300) &\color{red}\small\text{Substitute given sides}\\P &= 1200ft &\color{red}\small\text{ Multiply}\\\end{align*}

Both formulas will give the same answer for the perimeter of a square, which is 1200 feet in this example.

**Things to Remember**

- To calculate the perimeter of a rectangle or a square, add the lengths and the widths together.
- The formula for a square can be simplified because all the sides are the same.

### Practice Problems

- The top of a pizza box forms a square where each side is 35 cm. Find the perimeter of the square defined by this pizza box. (Video Solution
- A rectangular swimming pool has a length of 20 ft and a width of 12 ft. Find the perimeter of the rectangle defined by this swimming pool. (Solution
- The borders for the state of Colorado form a rectangle that measures about 360 miles long and 280 miles wide. Find the perimeter of the rectangle defined by this state. (Video Solution
- A rectangular flag has a length of 150 cm and a width of 120 cm. Find the perimeter of the rectangle defined by this flag. (Solution
- The cover of a book has a length of 5 in and a width of 8 in. Find the perimeter of the rectangle defined by this book cover. (Solution
- A basketball court is rectangular in shape with a length of 29 m and a width of 15 m. Find the perimeter of the rectangle defined by this court. (Solution