Introduction

In this lesson, you will learn that finding the area of a rectangle can also be seen as finding how many unit squares make up the rectangle.

\begin{align*} Area = Length \times Width \end{align*}

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

• Introduction to Area (03:52 mins) | Transcript

Solving for Area

Example 1
A rug is 4 feet long and 3 feet wide. What is the area of the rug? In this case, the unit square is 1 foot by 1 foot.

Figure 1

In order to calculate the area, multiply the length and the width. In this equation, the length is 4 feet, and the width is 3 feet.

\begin{align*}A &= (l)(w) &\color{red}\small\text{Formula for area of a rectangle}\\\\A &= (4ft)(3ft) &\color{red}\small\text{Substitute given terms}\\\\A &= 12(ft)(ft) &\color{red}\small\text{Multiply}\\\\A &=12ft^2 &\color{red}\small\text{Simplify}\\\\ \end{align*}

Figure 2

\\\begin{align*}\color{black}\large\text{Area of a Rectangle} = (length)(width)\\\end{align*}

\begin{align*} A&=(l)(w) \end{align*}

The unit for the area is units squared. The total area of the rug in example 1 is 12 feet squared, or \(12 ft^{2}\).

Example 2
A small space is 3 centimeters long by 2 centimeters wide. What is the area of the space?

Figure 3

Calculate the area by multiplying the length by the width. In this example, the length is 3 cm, and the width is 2 cm.

\begin{align*} A &= (l)(w) &\color{red}\small\text{Formula for area of a rectangle}\\\\ A &= (3cm)(2cm) &\color{red}\small\text{Substitute given terms}\\\\ A &= 6(cm)(cm) &\color{red}\small\text{Multiply}\\\\ A &=6cm^2 &\color{red}\small\text{Simplify}\\\\ \end{align*}

The area of this space is \(6 cm^{2}\).

Things to Remember

• You can only find the area if the two sides are measured in the same units.
• To calculate the area of a rectangle or a square use: \(A=l\times w\).

Practice Problems

1. Each side of a small square mirror is 12 cm long. Find the area of the mirror. (
   Solution

   x

   Solution: \(144\text{ cm}^{2}\)
   )
2. A rectangular rug measures 4 yd by 3 yd. Find the area of the rectangle defined by this rug. (
   Solution

   x

   Solution: \(12\text{ yd}^{2}\)
   )
3. The top of a rectangular desk has a length of 83 cm and a width of 33 cm. Find the area of the rectangle defined by this desk. (
   Solution

   x

   Solution: \(2739\text{ cm}^{2}\)
   Details:
   The sides of the desk have been measured in centimeters.
   
   When you find the area of a rectangle, you are trying to find out how many square units are in the rectangle. In this case, you are measuring the area in centimeters, so you want to find out how many one-centimeter by one-centimeter squares are in the rectangle.
   
   To find the area of the top of the desk, multiply the \({\color{Red}length}\) by the \({\color{Cyan}width}\).
   
   \({\color{Red} 83} \times {\color{Cyan} 33} = 2739\)
   
   The area of the top of the desk is \(2739\text{ cm}^{2}\).
   )
4. A dollar bill that is rectangular in shape has a length of 6 in and a width of 3 in. Find the area of the rectangle defined by this dollar bill. (
   Video Solution

   x

   Solution: \(18\text{ in}^{2}\)
   Details:
   

   
   (Introduction to Area #4 (01:13 mins) | Transcript)
   | Transcript)
5. The lengths of two adjacent sides of a rectangular envelope are 225 mm and 28 mm. Find the area of the rectangle defined by this envelope. (
   Video Solution

   x

   Solution: \(6300\text{ mm}^{2}\)
   Details:
   

   
   (Introduction to Area #5 (01:25 mins) | Transcript)
   | Transcript)
6. A rectangular garage door has a length of 16 ft and a height of 7 ft. Find the area of the rectangle defined by this garage door. (
   Solution

   x

   Solution: \(112\text{ ft}^{2}\)
   Details:
   The garage door has been measured in feet.
   
   When you find the area of a rectangle, you are trying to find out how many unit squares are in that rectangle. In this case, you are measuring the area in feet, so you want to find out how many 1 foot by 1 foot squares are in the rectangle.
   
   To find the area of the garage door you need to multiply the \({\color{Red}length}\) by the \({\color{Cyan}width}\).
   
   \({\color{Red} 16} \times {\color{Cyan} 7} = 112\)
   
   The area of the garage door is \(112\text{ ft}^{2}\).
   )

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