Converting units of area

The unit conversions for length can be used to calculate areas in different units.

The two squares have the same area.

Square 1

Area = \(1~\text{m} \times 1~\text{m}\)

Area = 1 m²

Square 2

Area = \(100~\text{cm} \times 100~\text{cm}\)

Area = 10,000 cm²

Since Square 1 and Square 2 have the same area, \(1~m^2 = 10,000~cm^2\)

Use the same method to convert cm² into mm².

Square 3

Area = \(1~\text{cm} \times 1~\text{cm}\)

Area = 1 cm²

1 cm² = 100 mm²

Square 4

Area = \(10~\text{mm} \times 10~\text{mm}\)

Area = 100 mm²

Since Square 3 and Square 4 have the same area, \(1~cm^2 = 100~mm^2\)

Convert 5.2 m² into cm².

\(1~\text{m}^2 = 100~\text{cm} \times 100~\text{cm} = 10,000~\text{cm}^2\)

\(5.2 \times 10,000 = 52,000~\text{cm}^\text{2}\)

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