Choosing and converting area units | Year 8

01 / LEARN

Understand the idea.

Square the conversion factor

An area conversion changes two dimensions. Since $1 m = 100 cm$ , a one-metre square measures $100 cm$ in each direction. It contains $100 \times 100 = 10 000$ squares of area $1 {cm}^{2}$ .

Square the length factor when converting square units. Thus $1 {cm}^{2} = 100 {mm}^{2}$ and $1 {km}^{2} = 1 000 000 m^{2}$ . Smaller units give a larger numerical value; converting back requires division by the same factor.

Useful area equivalences
Large unit	Equivalent smaller area
1 cm²	100 mm²
1 m²	10,000 cm²
1 hectare	10,000 m²
1 km²	1,000,000 m²

Choose a sensible unit

Choose units that suit the surface: square millimetres or centimetres for small objects, square metres for floors, hectares for land and square kilometres for large regions. The surface stays the same size when its unit changes.

Before multiplying dimensions, express both lengths in the same unit. A rectangle $2 m$ by $50 cm$ is $2 m$ by $0.5 m$ . Its area is $1 m^{2}$ ; multiplying the unconverted numerical values does not give square metres.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

From metres to centimetres

Convert 2.4 m² to cm².

Worked solution

1
Establish the square-unit factor.
$1 m^{2} = {(100 cm)}^{2} = 10 000 {cm}^{2}$
Both dimensions of the unit square change by a factor of 100.
2
Multiply by the number of square metres.
$2.4 \times 10 000 = 24 000$
Each square metre contains ten thousand square centimetres.
3
Attach the destination unit.
$2.4 m^{2} = 24 000 {cm}^{2}$
Using a smaller square unit increases the numerical value without changing the area.

Answer

24,000 cm².

EXAMPLE 02

Mixed length units

A poster is 80 cm wide and 1.2 m high. Find its area in m².

Worked solution

1
Express the width in metres.
$80 cm = \frac{80}{100} m = 0.8 m$
The requested square-metre answer requires matching metre dimensions.
2
Multiply width by height.
$A = 0.8 \times 1.2 = 0.96 m^{2}$
Multiplying two metre lengths produces square metres.
3
Check using centimetres.
$\begin{aligned} 1.2 m & = 120 cm \\ 80 \times 120 & = 9600 {cm}^{2} \\ \frac{9600}{10 000} & = 0.96 m^{2} \end{aligned}$
Calculating in a second consistent unit gives the same area.

Answer

0.96 m².

03 / YOUR TURN

Try it yourself.

Check your understanding

How many square millimetres are in 5 cm²?

Show answer & reasoning

500 mm².

Each centimetre contains 10 millimetres, so $1 {cm}^{2} = 10 \times 10 = 100 {mm}^{2}$ . Therefore $5 {cm}^{2} = 500 {mm}^{2}$ .

Keep practising

6 worksheet questions · 14 marks

Open worksheet Worked solutions

Read the questions online

Convert 7 cm² to mm².
2 marks
Convert 0.6 m² to cm².
2 marks
Convert 35,000 cm² to m².
2 marks
Convert 2.5 hectares to m².
2 marks
A board is 1.5 m long and 40 cm wide. Find its area in m².
3 marks
A student says 0.03 km² is 30 m². Correct the answer and explain the conversion.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Convert 7 cm² to mm².
2 marks
$7 \times 100 = 700$ mm².
700 mm².
Convert 0.6 m² to cm².
2 marks
$0.6 \times 10000 = 6000$ cm².
6000 cm².
Convert 35,000 cm² to m².
2 marks
$35000 \div 10000 = 3.5$ m².
3.5 m².
Convert 2.5 hectares to m².
2 marks
$2.5 \times 10000 = 25000$ m².
25,000 m².
A board is 1.5 m long and 40 cm wide. Find its area in m².
3 marks
40 cm is 0.4 m.
$A = 1.5 (0.4) = 0.6$ m².
0.6 m².
A student says 0.03 km² is 30 m². Correct the answer and explain the conversion.
3 marks
A square kilometre contains $1000 \times 1000 = 1000000$ m².
$0.03 \times 1000000 = 30000$ m².
30,000 m².

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Circumference and area of circles; perimeter/area of composite shapes; choosing and converting area units; cross-sections of prisms; prism volume and capacity; mixed measurement applications.

Official curriculum source ↗

In this lesson

Understand the idea.

Square the conversion factor

Choose a sensible unit

See the method in action.

From metres to centimetres

Establish the square-unit factor.

Multiply by the number of square metres.

Attach the destination unit.

Mixed length units

Express the width in metres.

Multiply width by height.

Check using centimetres.

Try it yourself.

Check your understanding

Keep practising