Area and Perimeter

Lengths, Areas and Volumes

The conversions to know

Metric conversions all work by multiplying or dividing by a power of ten

Measure	Conversions
Length	1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m
Mass	1 g = 1000 mg, 1 kg = 1000 g, 1 tonne = 1000 kg
Capacity	1 litre = 1000 ml, 1 cl = 10 ml
Volume to capacity	1 ml = 1 cm³, 1 litre = 1000 cm³, 1 m³ = 1000 litres

Decide between multiplying and dividing by asking whether the count of units should go up or down
Changing to a smaller unit gives a bigger number, so multiply; changing to a larger unit gives a smaller number, so divide
Awkward conversions are safer in stages, so centimetres to kilometres goes through metres first

Squared and cubed units

Area units are squared, so the conversion factor is squared too
Volume units are cubed, so the conversion factor is cubed
- 1 cm² = 10² mm² = 100 mm²
- 1 m² = 100² cm² = 10 000 cm²
- 1 km² = 1000² m² = 1 000 000 m²
- 1 cm³ = 10³ mm³ = 1000 mm³
- 1 m³ = 100³ cm³ = 1 000 000 cm³
Picture a square metre as a square measuring 100 cm by 100 cm, which makes the 10 000 obvious rather than something to memorise
The syllabus names conversion between area units and between volume and capacity explicitly, so both are examinable

Exam tip

Square the conversion factor for an area and cube it for a volume. Changing m² to cm² by multiplying by 100 instead of 10 000 is the commonest error in this topic.

Worked example

Converting an area

Convert 2.5 m² into cm², and 45 000 cm² into m².

Solution:

One metre is 100 cm, so one square metre is 100 × 100 = 10 000 cm²
Changing to the smaller unit means multiplying
2.5 × 10 000 = 25 000 cm²
Going the other way means dividing by the same factor
45 000 ÷ 10 000 = 4.5 m²
Check: 4.5 × 10 000 = 45 000