The area of a shape can be measured by comparing the shape to squares of a fixed size.^[2] 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.^[3] 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.

For a cube, the lateral surface area would be the area of the four sides. If the edge of the cube has length a, the area of one square face A_face = a ⋅ a = a². Thus the lateral surface of a cube will be the area of four faces: 4a².

More generally, the lateral surface area of a prism is the sum of the areas of the sides of the prism.^[1] This lateral surface area can be calculated by multiplying the perimeter of the base by the height of the prism.^[2]

For a right circular cylinder of radius r and height h, the lateral area is the area of the side surface of the cylinder: A = 2πrh.

For a pyramid, the lateral surface area is the sum of the areas of all of the triangular faces but excluding the area of the base.

For a cone, the lateral surface area would be π r⋅l where r is the radius of the circle at the bottom of the cone and l is the lateral height (the length of a line segment from the apex of the cone along its side to its base) of the cone (given by the Pythagorean theorem l=√r² + h² where h is the height of the cone)

A general definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory, which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski content of a surface.