Area

Area (English: area) is a measure of the extent of a flat space with two dimensions, such as the interior of a shape, a plot, or land. It is defined as the two-dimensional quantity contained within a figure.

Area is one of the basic measurements in geometry, distinct from length (one dimension) and volume (three dimensions). It is used in mathematics, construction, farming, and land measurement.

Units of area measurement

The international unit of area is the square metre (m²), meaning the area of a square with each side one metre long. Other common units include the square centimetre (cm²), square kilometre (km²), hectare (10,000 m²), and are (100 m²). Other systems use square feet or acres.

Calculating area of common shapes

The area of a rectangle is length multiplied by width. The area of a square (sides equal) is one side multiplied by itself. The area of a triangle is half the base multiplied by the height. The area of a circle is π multiplied by the square of the radius. For irregular shapes, area is calculated by dividing them into simpler pieces and then adding the areas together.

Area in higher geometry and calculus

For shapes without straight sides, area is calculated using integration, a mathematical method of summing infinitesimally small pieces. There also exists surface area, which measures the extent of the outer surface of a three-dimensional object, such as a sphere or cylinder.