# Definition:Area

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## Definition

**Area** is the measure of the extent of a surface.

It has $2$ dimensions and is specified in units of length squared.

Hence the term *square* as a general vague term for a quantity in $2$ dimensions.

### Dimension

**Area** is a dimension of measurement of physics.

The dimension of **area** is $L^2$: length squared.

## Units

- The SI unit of
**area**is the square metre $\mathrm m^2$. - The CGS unit of
**area**is the square centimetre $\mathrm {cm}^2$.

Thus:

- $1 \ \mathrm m^2 = 10^4 \ \mathrm {cm}^2$

## Axioms of Area

When discussing areas of surfaces, we usually take the following statements to be axiomatic:

- $(2) \quad$ Let a surface be divided into a finite number of smaller non-overlapping surfaces.
- Let the smaller surfaces cover the entire larger surface.
- Then the sum of the areas of the smaller surfaces equals the area of the larger surface.

- $(3) \quad$ Equal surfaces have equal areas.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**area** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**area** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**area**