Area is a fundamental measure of a region's size on a surface, serving as the two-dimensional analogue to a curve's length or a solid's volume. It distinguishes between plane area for flat shapes and surface area for the boundary of three-dimensional objects.

This measurement is typically quantified by comparing a shape to squares of a fixed size, with the square metre (m²) established as the standard unit within the International System of Units (SI).

While simple shapes like rectangles and triangles have well-known formulas, areas of complex polygons are found by division, and computing areas for shapes with curved boundaries significantly contributed to the historical development of calculus. Notably, ancient Greeks computed surface area formulas for basic 3D shapes.

Beyond geometry, area plays a crucial role in modern mathematics, influencing concepts in linear algebra and differential geometry, and can be formally defined through a set of axioms that ensure its consistent and rigorous application.