<P> 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 the length of a curve (a one - dimensional concept) or the volume of a solid (a three - dimensional concept). </P> <P> 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 m), 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 . </P> <P> There are several well - known formulas for the areas of simple shapes such as triangles, rectangles, and circles . Using these formulas, the area of any polygon can be found by dividing the polygon into triangles . For shapes with curved boundary, calculus is usually required to compute the area . Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus . </P> <P> For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area . Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus . </P>

Rule for finding the area of a square