Choosing and converting area units | Year 8

01 / LEARN

The idea, step by step

Square the conversion factor

One metre is 100 centimetres. A square measuring 1 m on each side therefore measures 100 cm by 100 cm. Its area is $100 \times 100 = 10000$ cm². The factor for square units is not merely 100.

Larger square units contain many smaller squares. Multiply when converting to smaller units, and divide when converting to larger units. Write a unit at each step so the change remains visible.

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

Use mm² or cm² for small surfaces, m² for floors and gardens, hectares for large land areas, and km² for very large regions. The object has the same area whichever valid unit is chosen; only the numerical value changes.

Convert all dimensions to a consistent length unit before applying a formula. A rectangle 2 m by 50 cm is $2 \times 0.5 = 1$ m², not 100 m².

A common trap

Converting 3 m² to 300 cm².

Instead: The length factor 100 acts twice: $3 \times 10000 = 30000$ cm².

02 / WORKED EXAMPLES

See the thinking

Example 1

From metres to centimetres

Convert 2.4 m² to cm².

$1$ m² equals $10000$ cm².
Multiply: $2.4 \times 10000 = 24000$ .

24,000 cm².

Example 2

Mixed length units

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

Convert 80 cm to 0.8 m.
Use matching units: $A = 0.8 \times 1.2 = 0.96$ m².
Alternatively, 80 cm × 120 cm is 9600 cm², which gives the same result after division by 10000.

0.96 m².

Check your understanding

How many square millimetres are in 5 cm²?

Show answer

500 mm².

There are $10 \times 10 = 100$ mm² in 1 cm²; multiply 5 by 100.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF 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 ↗

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