Converting units of area
A square unit is the square of the length. 1 m is 100 cm, but 1 m² is not 100 cm².
A square metre
A square 1 metre on each side has an area of 1 square metre, written 1 m². We know that 1 m = 100 cm.
How many square centimetres fit in 1 square metre?
What this lesson covers
The idea
An area unit converts by the square of the length conversion: if one length unit equals k of another, then one square unit equals k² square units of the other.
A square metre
A square 1 metre on each side has an area of 1 square metre, written 1 m². We know that 1 m = 100 cm.
How many square centimetres fit in 1 square metre?
- 100 cm²
- 1,000 cm²
- 10,000 cm²
Count the squares
In the first tab, a big square is cut into rows of small squares. Press + and − to change how many small units make one big unit, and make the big square hold 25, 64 and 144 small squares. Then zoom into the square metre in the second tab.
Square the conversion
An area unit converts by the square of the length conversion: if one length unit equals k of another, then one square unit equals k² square units of the other.
If one side of the big square is k small units, the big square has k rows of k small squares: k × k = k². With k = 5 that was 25 squares, with k = 8 it was 64 and with k = 12 it was 144.
1 ft = 12 in, so 1 ft² = 12 × 12 = 144 in². And 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm², not 100.
The book uses 1 in = 2.54 cm, so 1 in² = 2.54 × 2.54 = 6.4516 cm² and 10 in² = 64.516 cm². To go the other way, divide: 161.29 ÷ 6.4516 = 25, so 161.29 cm² is 25 in².
Notes
An area unit converts by the square of the length conversion: if one length unit equals k of another, then one square unit equals k² square units of the other.
Check yourself
One side of a big square is 12 small units. How many small squares fill the big square?
Answer: 144
12 rows of 12 small squares is 12 × 12 = 144, like 1 ft² = 144 in².
How many cm² are there in 3 m²?
Answer: 30000
1 m² = 100 × 100 = 10,000 cm², so 3 m² = 3 × 10,000 = 30,000 cm².
1 km = 1000 m. How many square metres are in 1 square kilometre?
1 acre = 43,560 ft². A plot has an area of 1,30,680 ft². How many acres is it?
Answer: 3
1,30,680 ÷ 43,560 = 3, so the plot is 3 acres. (3 × 43,560 = 1,30,680.)
- 1,000 m². That is the number of metres in a kilometre. For area, multiply it by itself: 1000 × 1000.
- 10,000 m². That is 100 × 100. Here 1 km = 1000 m, so the factor is 1000 × 1000.
- 1,00,000 m². That is 1000 × 100. Both sides are 1000 m long, so multiply 1000 × 1000.
- 10,00,000 m² — correct. Yes! 1000 × 1000 = 10,00,000 (ten lakh) square metres.