Units of area · Martinとコード

A square metre is bigger than you think

How many square centimetres are in one square metre? A metre has 100 cm, so… 100? No. Ten thousand.

This is the trickiest conversion in all of year-5 maths and today you will crack it so it never catches you again.

A square metre is a square 1 m × 1 m. Convert the sides to centimetres: 100 cm × 100 cm. And you work out the area as you can from the last lesson: 100 × 100 = 10 000 cm².

See what happened? The length conversion (×100) was used twice — once for each side of the square. With units of area all the conversion jumps are therefore squared: where length jumps a hundred times, area jumps ten thousand times.

Between neighbouring units of area (mm² → cm² → dm² → m²) there is therefore always a jump of ×100, not ×10. Once you get it through a square — and then you just shift the point by two places instead of one.

Tereza is helping mum pick a carpet for a room 4 m × 3 m. “We need 12 square metres,” Tereza counts. In the web shop she finds a little rug with the figure “7 500 cm²”. “That sounds like a lot! Seven and a half thousand!” Mum smiles: “And how many square metres is that?” Tereza divides: 7 500 : 10 000 = 0.75. “Not even a square metre?! That is a doormat, not a carpet!” Big numbers in small units can confuse — that is why area conversions are worth knowing. Into the basket in the end goes an honest carpet 4 × 3 metres.

💡

An area conversion = a length conversion twice. Metres to centimetres is ×100, so m² to cm² is ×100 ×100 = ×10 000. The point jumps TWO places for each step.

The ladder of units of area

Line the units up as a ladder — between neighbouring rungs there is always ×100:

Unit	It is a square	In the smaller unit
1 cm²	1 cm × 1 cm	100 mm²
1 dm²	10 cm × 10 cm	100 cm²
1 m²	100 cm × 100 cm	100 dm² = 10 000 cm²

Direction down (to smaller units) = multiplying: 3 m² = 3 × 10 000 = 30 000 cm². A smaller unit → more pieces → a bigger number.

Direction up (to bigger units) = dividing: 500 cm² = 500 : 100 = 5 dm². A bigger unit → fewer pieces → a smaller number.

In practice it is shifting the point by two places for each rung of the ladder: 2.5 m² → 250 dm² → 25 000 cm².

For land two more units are used that you know from the news and from a cottage: an are (a) = 100 m² (a square 10 × 10 m, about a garden) and a hectare (ha) = 100 ares = 10 000 m² (a square 100 × 100 m, about a football pitch with the surroundings). Here too everything jumps by hundreds — the area ladder is a hundreds ladder from top to bottom.

A check after every conversion: does the result make sense? A carpet for a room cannot have 0.75 m² — Tereza spotted that before she converted anything.

Convert 3.2 m² to cm²

From m² to cm² there are two rungs of the ladder (m² → dm² → cm²), each ×100.

3.2 × 100 = 320 (those are dm²) 320 × 100 = 32 000 cm²

Or at once: 3.2 × 10 000 — the point four places to the right.

A sense check: a smaller unit, so a MUCH bigger number. A table top 3.2 m² really holds tens of thousands of centimetre squares.

Convert 45 000 cm² to m²

Direction up — I divide. Two rungs of a hundred, so : 10 000.

45 000 : 10 000 = 4.5 m².

The point jumped four places to the left.

Sense: 4.5 m² is for example the area of a bigger bed. If I by mistake only divided by a hundred, 450 “m²” would come out — the area of a decent flat from one bed. That is how a sense check catches conversion mistakes.

A garden in ares

Grandma’s garden is a rectangle 25 m × 20 m. How many ares is that?

Area: S = 25 × 20 = 500 m².

Conversion: 1 are = 100 m², so 500 : 100 = 5 ares.

And for a picture of a hectare: 500 m² is 0.05 ha — a twentieth of a hectare. A football pitch would swallow grandma’s garden twenty times. Ares for gardens, hectares for fields and woods.

⚠️

1 m² is NOT 100 cm². A metre has a hundred centimetres — a line. But a SQUARE metre is a surface: 100 × 100 = 10 000 cm². With area every length conversion is counted twice. Who converts area by one place of the point mixes a line with a surface.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. スタート with ten. When it goes well, add more.

Practise length conversions — they are the base from which area jumps are built (×100 on length = ×10 000 on area). The answer is a number.

Practise the questions

On paper

Draw yourself a ladder mm² – cm² – dm² – m² with arrows ×100 and keep it to hand.

Convert: 5 m² to dm², 5 m² to cm², 700 cm² to dm², 250 000 cm² to m².
Draw a square 1 dm × 1 dm (10 × 10 cm) and split it into centimetre squares with a grid. How many are there? Write: 1 dm² = ? cm².
A room has a floor 4 m × 3.5 m. Work out the area in m² and convert to dm². How many square tiles 50 cm × 50 cm would cover the floor? (Hint: one tile = 2 500 cm².)
Order from the smallest area: 2 m², 25 000 cm², 180 dm². (Convert everything to dm².)

Now you 💪

I know why 1 m² = 10 000 cm², and I can show it with the calculation 100 × 100.
I convert between neighbouring units of area with a jump of ×100 (the point by two places).
I can estimate whether the result is reasonable — a carpet is not 0.75 m².

✅

Done when: You convert units of area both ways through the hundreds ladder and you understand why a length conversion is counted twice with surfaces.

What to take from this lesson

Units of area jump by ×100: mm² → cm² → dm² → m².
1 m² = 10 000 cm², because 100 cm × 100 cm. A length conversion twice!
To smaller units you multiply (a bigger number), to bigger you divide (a smaller number).
Are = 100 m² (a garden), hectare = 10 000 m² (a pitch). Here too everything by hundreds.
A sense check: the converted area must match the thing it describes.