Lesson 2: Area - Area of Rectangles

   Constructing Knowledge

Recall that the formula for the area of a rectangle is:

Arearectangle = length × width

Arearectangle = lw

When using a formula to calculate area, follow these basic steps:

  1. State the formula being used to solve the problem.
  2. Substitute known values for the variables.
  3. Solve for the unknown (remember to include proper squared units in your answer).

Remember that with all area calculations, all dimensions must be in the same unit of measure prior to substituting their values into the formula.

   Multimedia

A video demonstrating calculating the area of a rectangle is provided.



EXAMPLE 1

Determine the area of a rectangle with a width of 1.5 m and a length of 9 ft, to the nearest hundredth of a square metre.



Solution


Step 1: Change the measurement that is in feet to metres.

\(\begin{align} \frac{y}{9\,\text{ft}}&=\frac{1\,\text{m}}{3.281\,\text{ft}} \\ \\ \frac{y}{\cancel{9\,\text{ft}}}\times {\color{red}{\cancel{9\,\text{ft}}}}&=\frac{1\,\text{m}}{3.281\cancel{\text{ft}}}\times {\color{red}{9\cancel{\text{ft}}}} \\ \\ y&=\frac{1\,\text{m}\times 9}{3.281} \\ \\ y&=2.74\,\text{m} \\ \end{align}\)

Step 2: Calculate the area of the rectangle using 2.74 m as the length and 1.5 m as the width.

Arearectangle = lw
= 2.74 m × 1.5 m
= 4.11 m2

The rectangle's area is 4.11 m2.

EXAMPLE 2

The square footage of a rectangular hair salon is 2 400 ft². If the salon is 30 ft wide, how long is the salon?

Solution


\(\begin{align} \text{Area}_{\text{rectangle}}&=lw \\ \\ 2400\,\text{ft}^2&=l\times 30\,\text{ft} \\ \\ \frac{2400\,\text{ft}^2}{30\,\text{ft}}&=\frac{l\times \cancel{30\,\text{ft}}}{\cancel{30\,\text{ft}}} \\ \\ 80\,\text{ft}&=l \end{align}\)

The hair salon is 80 ft long.


Now, it is your turn! Complete the questions in your Chapter 7, Lesson 2 Practice Makes Perfect that refer to Area of Rectangles.



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