Definition:Area

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:

$(1) \quad$ The area of a square with a side of length one unit is defined to be one square unit.

$(2) \quad$ 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

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): area
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): area
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): area
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): area