Area is length squared — and that catches people out
Because area scales with the square of length, the conversion factor between two area units is the square of their length factor. One foot is 0.3048 metres, so one square foot is 0.3048², or 0.09290304 square metres. Using the length factor by mistake understates the area by a factor of more than three.
The same principle explains why a 12×12 ft room is 144 ft², not 24. And why upgrading from a 20 ft² to a 30 ft² sign costs half as much again in material, but a room extension from 10×10 to 15×15 more than doubles the floor.
Acres, hectares and the football pitch
The acre began as the area a yoke of oxen could plough in a day — one furlong long by one chain wide, which is why it is 43,560 square feet rather than a round number. The hectare is the metric equivalent and is a clean 10,000 square metres, about 2.47 acres.
For a sense of scale: a full-size football pitch is roughly 1.8 acres or 0.7 hectares, and a square mile is exactly 640 acres, which is why American land was historically parcelled into 640-acre sections.