Top left is the height and top right is the width, both in metres. The card between them works out the area in metres. The two cards below turn the height and the width into centimetres (H and W), and the card between them works out the area in centimetres.
1 m is 100 cm
Start with length. 1 m = 100 cm, so to go from m to cm you multiply by 100. The two bottom corner cards on the board show "×100".
So what is 1 m²?
1 m² is the area of a square 1 m high and 1 m wide. Area is height × width: 1 × 1 = 1, so 1 m². The top middle card on the board shows "= 1".
Both sides are 100 cm
Now measure the same square in centimetres.
- Height — 1 m = 100 cm
- Width — 1 m = 100 cm
- Area — 100 × 100 = 10,000 cm²
The bottom middle card shows "= 10,000" too. The length goes up 100 times, but the area goes up 100 × 100 = 10,000 times, because the height and the width both go up 100 times.
Why not 100 cm²?
It is tempting to think "1 m = 100 cm, so 1 m² = 100 cm²". But 100 cm² is the area of a square 10 cm on each side (10 × 10 = 100). A 10 cm side is only a tenth of a metre.
A 1 m square fits 10 of these 10 cm squares across and 10 down: 100 of them in all. And 100 lots of 100 cm² make 10,000 cm².
Try it yourself
Change the height and width on the board.
| Height | Width | Area (m²) | Height × width (cm) | Area (cm²) |
|---|---|---|---|---|
| 1 m | 1 m | 1 m² | 100 × 100 | 10,000 cm² |
| 2 m | 1 m | 2 m² | 200 × 100 | 20,000 cm² |
| 2 m | 3 m | 6 m² | 200 × 300 | 60,000 cm² |
| 0.5 m | 1 m | 0.5 m² | 50 × 100 | 5,000 cm² |
Whatever the shape, the number in cm² is 10,000 times the number in m². 2 m² is 20,000 cm², 6 m² is 60,000 cm², and 0.5 m² is 5,000 cm².
Put in one line: 1 m² = (100 cm)² = 10,000 cm². The ² (squared) means the same number is multiplied in twice — the ×100 once for the height and once for the width.
See also — When converting cm to m, do you multiply or divide by 100? For lengths, the direction decides whether it is ÷100 or ×100.