Area is the quantity that expresses the extent of a two-dimensional figure or shape , or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape , or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analog of thelength of a curve (a one-dimensional concept ) or the volume of a solid (a three-dimensional concept ).
The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics , the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number .
There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, andcircles . Using these formulas, the area of any polygon can be found by dividing the polygon into triangles.