Lesson 4: Conversions Between SI and Imperial - Area Conversion

   Constructing Knowledge

As you have already seen in this chapter, both SI and imperial units are commonly used. For example you might calculate the area of a wall in metric units, only to discover that the area covered by a can of paint is given in imperial units. Converting between area units will help you determine how many cans of paint are required.

Use proportional reasoning to convert area between SI and Imperial units.

Area: Imperial to SI
Imperial SI
1 square inch 6.45 square centimetres
1 square foot 0.09 square metres
1 square yard 0.836 square metres
1 square acre 0.405 hectare
Area: SI to Imperial
SI Imperial
1 square centimetre 0.394 square inches
1 square metre 10.76 square feet
1 square metre 1.196 square yards
1 hectare 2.471 acres

EXAMPLE 1

A house is listed as being 140 square metres. What is the size of the house in square feet?

Solution


\(\begin{align} \frac{y}{140\,\text{m}^2}&=\frac{1\,\text{ft}^2}{0.09\,\text{m}^2} \\ \\ \frac{y}{\cancel{140\,\text{m}^2}}\times {\color{red}{\cancel{140\,\text{m}^2}}}&=\frac{1\,\text{ft}^2}{0.09\cancel{\text{m}^2}}\times \color{red}{140\cancel{\text{m}^2}} \\ \\ y&=\frac{1\,\text{ft}^{2}\times 140}{0.09} \\ \\ y&=\frac{140\,\text{ft}^2}{0.09} \\ \\ y&=1 555.6\,\text{ft}^2 \\ \end{align}\)

The size of the house is approximately 1 555.6 ft2.

   Constructing Knowledge

There may be times when it is necessary to calculate an area conversion ratio from a linear conversion ratio. This is often necessary when the desired conversion ratio is not readily available. To calculate the area conversion ratio, square both the numerator and the denominator of the linear conversion ratio.

   Multimedia

A video demonstrating area conversions between the SI and Imperial system is provided.



EXAMPLE 2

A large computer chip's area is 450 mm2. How many square inches is the computer chip? Round the answer to three decimal places.

Solution


Step 1: Calculate the conversion ratio for square mm and square inches.

\(\begin{align} \text{conversion ratio}&={\left(\frac{1\,\text{in}}{25.4\,\text{mm}}\right)}^2 \\ \\ &=\left(\frac{1\,\text{in}\times 1\,\text{in}}{25.4\,\text{mm}\times 25.4\,\text{mm}}\right) \\ \\ &=\frac{1\,\text{in}^2}{645.16\,\text{mm}^2} \\ \end{align}\)

Step 2: Calculate the number of square inches in 450 mm2.

\(\begin{align} \frac{y}{450\,\text{mm}^2}&=\frac{1\,\text{in}^2}{645.16\,\text{mm}^2} \\ \\ \frac{y}{\cancel{450\,\text{mm}^2}}\times {\color{red}{\cancel{450\,\text{mm}^2}}}&=\frac{1\,\text{in}^2}{645.16\cancel{\text{mm}^2}}\times \color{red}{450\cancel{\text{mm}^2}} \\ \\ y&=\frac{1\,\text{in}^{2}\times 450}{645.16} \\ \\ y&=\frac{450\,\text{ft}^2}{645.16} \\ \\ y&=0.698\,\text{in}^2 \\ \end{align}\)

The computer chip is 0.698 in2.


Now, it is your turn! Complete the questions in your Chapter 5, Lesson 4 Practice Makes Perfect that refer to Area Conversion.



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