Units of Area: The Conversion Ladder, Hectares and Ares

Units of area measure the size of a surface, with the square metre (m²) as the base unit. The topic is taught in Year 4 and differs from units of length in one important way: its ladder steps by 100, not 10.

Why 100 and Not 10

This is the heart of the topic, and it is almost never explained.

1 metre = 10 decimetres. But area has two dimensions, length and width. So:

1 m² = 10 dm × 10 dm = 100 dm²

Not 10. Each step up or down the ladder is a factor of 100 because the conversion applies twice — once to length and once to width. A child who understands this never needs to memorise the table at all; they can rebuild it any time.

The Area Ladder

km² → hm² → dam² → m² → dm² → cm² → mm²

• Each step down → multiply by 100
• Each step up → divide by 100

Hectares, Ares and Centiares

These are used for land and fields, and appear most often in word problems:

Put simply: a hectare is a hm², an are is a dam², a centiare is a m². Those three lines cover every land-area question.

Worked Conversions

5 m² = ? cm² Two steps down → 5 × 100 × 100 = 50,000 cm²

2.5 hectares = ? m² 1 ha = 10,000 m² → 2.5 × 10,000 = 25,000 m²

300 dm² = ? m² One step up → 300 ÷ 100 = 3 m²

A Worked Word Problem

A rectangular garden measures 40 m × 25 m. What is its area in ares?

• Area = 40 × 25 = 1,000 m²
• 1 are = 100 m² → 1,000 ÷ 100 = 10 ares

The order is always the same: work out the area in the original units first, then convert. Converting length and width first also works, but leaves more room for error.

The Mistakes That Actually Cost Marks

1. Using steps of 10 instead of 100. The number one cause, and it puts the answer out by a factor of ten for every step. Children who have just mastered the length ladder are the most vulnerable, because the reflex carries the 10 across.

2. Confusing hectares with ares. A hectare is 10,000 m² and an are is 100 m² — a hundredfold difference. If a field-area answer looks strange, this is usually why.

3. Converting the units before calculating the area and then forgetting that the conversion has to happen twice.

4. Writing the unit without the square. Area is always in square units. An answer of "12 m" for an area is wrong even when the number is right.

5. Assuming volume units also step by 100. Volume has three dimensions, so its ladder steps by 1,000. See solid shapes.