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.
Solving for Area
A unit square is simply a square where each side has a length of one unit. You can only find the area of a rectangle if the two sides are measured in the same units, this is because the area is measured in squared units.
Example 1
A room is 4 meters long and 3 meters wide. What is the area of the room? In this case, the unit square is 1 meter by 1 meter.
Figure 1
In order to calculate the area, multiply the length and the width. In this equation, the length is 4 meters, and the width is 3 meters.
\begin{align*}A &= (l)(w) &\color{red}\small\text{Formula for area of a rectangle}\\\\A &= (4m)(3m) &\color{red}\small\text{Substitute given terms}\\\\A &= 12(m)(m) &\color{red}\small\text{Multiply}\\\\A &=12m^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 room is 12 meters squared, or \(12 m^{2}\).
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
- Each side of a small square mirror is 12 cm long. Find the area of the mirror. (Solution
- A rectangular rug measures 4 yd by 3 yd. Find the area of the rectangle defined by this rug. (Solution
- 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
- 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
- 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
- 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