Metric Units for Area
Area is measured in square units such as \(\text{mm}^2\), \(\text{cm}^2\), \(\text{m}^2\), hectares and \(\text{km}^2\). This NSW Year 7 maths subtopic (NESA outcome MA4‑ARE‑C‑01) shows where each conversion fact comes from: a 1 cm square is 10 mm by 10 mm, so \(1\text{ cm}^2 = 100\text{ mm}^2\).
You will make area conversions by multiplying or dividing by 100, 10 000 or 1 000 000, learn that a hectare is a square 100 m by 100 m, pick a sensible unit for a phone screen, a classroom floor or a farm, and solve carpet and tiling problems, such as how many 20 cm tiles cover a laundry floor. It is part of Year 7 Area and Volume.
Every question with a fully worked solution.
- Metric Units for Area - Video - Units of Area Watch
Theory
Area is the amount of surface a shape covers, measured in square units. Each unit is a square whose sides are one unit of length long, so \(1~\text{cm}^2 = 10~\text{mm} \times 10~\text{mm} = 100~\text{mm}^2\). This Year 7 maths page gives every area conversion, the conversion chart and the hectare.
\(1~\text{cm}^2\) (one square centimetre) is the area of a square \(1\) cm by \(1\) cm. Since \(1\) cm \(= 10\) mm, that square is \(10\) mm by \(10\) mm: \(1~\text{cm}^2 = 10 \times 10~\text{mm}^2 = 100~\text{mm}^2\).
The same idea gives every fact. A \(1\) m square is \(100\) cm by \(100\) cm: \(1~\text{m}^2 = 10\,000~\text{cm}^2\). A hectare (ha) is a square \(100\) m by \(100\) m: \(1~\text{ha} = 10\,000~\text{m}^2\). A \(1\) km square is \(1000\) m by \(1000\) m: \(1~\text{km}^2 = 1\,000\,000~\text{m}^2 = 100~\text{ha}\).
Bigger unit to smaller unit: multiply (there are more of the smaller squares). Smaller unit to bigger unit: divide (there are fewer of the bigger squares).
Choose the unit that gives a sensible number: mm\(^2\) for the head of a drawing pin, cm\(^2\) for a fingernail or a postage stamp, m\(^2\) for a bedroom floor or a dance mat, ha for a farm paddock or school grounds (a rugby field with its in-goal areas is about \(1\) ha), km\(^2\) for a national park or a city.
Area facts:
How to convert units of area
- Find both units on the area chart.
- Multiply to go to a smaller unit; divide to go to a bigger unit.
- Take two steps if there is no single arrow.
- Or change the side lengths first, then find the area in the new unit.
| \(5.8 \times 10\,000\) | \(=\) | \(58\,000\) |
\(58\,000~\text{cm}^2\)
(i) \(6.5~\text{cm}^2 = \) ___ mm\(^2\)
(ii) \(0.3~\text{m}^2 = \) ___ cm\(^2\)
| \(6.5 \times 100\) | \(=\) | \(650\) |
| \(0.3 \times 10\,000\) | \(=\) | \(3000\) |
(i) \(650~\text{mm}^2\)
(ii) \(3000~\text{cm}^2\)
(i) \(2750~\text{mm}^2 = \) ___ cm\(^2\)
(ii) \(48\,000~\text{m}^2 = \) ___ ha
(iii) \(3600~\text{mm}^2 = \) ___ m\(^2\)
| \(2750 \div 100\) | \(=\) | \(27.5\) |
| \(48\,000 \div 10\,000\) | \(=\) | \(4.8\) |
| \(3600 \div 100\) | \(=\) | \(36\) |
| \(36 \div 10\,000\) | \(=\) | \(0.0036\) |
(i) \(27.5~\text{cm}^2\)
(ii) \(4.8\) ha
(iii) two steps, mm\(^2\) to cm\(^2\) to m\(^2\): \(0.0036~\text{m}^2\)
| \(1.2 \times 1000\) | \(=\) | \(1200\) |
| \(1200 \times 800\) | \(=\) | \(960\,000\) |
| \(960\,000 \div 10\,000\) | \(=\) | \(96\) |
\(96\) ha. Check in km\(^2\): \(1.2 \times 0.8 = 0.96~\text{km}^2 = 96\) ha.
| \(2 \times 10\,000\) | \(=\) | \(20\,000\) |
| \(20 \times 20\) | \(=\) | \(400\) |
| \(20\,000 \div 400\) | \(=\) | \(50\) |
\(50\) plots. Check: \(1\) ha is \(5 \times 5 = 25\) plots.
| \(400 \times 150\) | \(=\) | \(60\,000\) |
| \(25 \times 25\) | \(=\) | \(625\) |
| \(60\,000 \div 625\) | \(=\) | \(96\) |
Work in cm: \(96\) tiles.
| \(0.7 \times 10\,000\) | \(=\) | \(7000\) |
| \(720\,000 \div 100\) | \(=\) | \(7200\) |
In cm\(^2\): \(6500\), \(7000\), \(7200\). So \(6500~\text{cm}^2\), \(0.7~\text{m}^2\), \(720\,000~\text{mm}^2\).
Common pitfalls
Frequently asked questions
How many square millimetres are in a square centimetre?
\(100\), because the square is \(10\) mm by \(10\) mm.
How many square centimetres are in a square metre?
\(10\,000\), because the square is \(100\) cm by \(100\) cm.
What is a hectare?
The area of a square \(100\) m by \(100\) m: \(10\,000~\text{m}^2\).
How many hectares are in a square kilometre?
\(100\).
Which unit should I use for a farm?
Hectares.