# Surface area

(Redirected from Surface Area)

Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve.

For polyhedra (objects with flat polygonal faces) the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of the surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.

##  Common formulas

Surface areas of common solids
Shape Variables
Cube s = side length
Rectangular prism = length, w = width, h = height
Sphere r = radius of sphere
Spherical lune r = radius of sphere, θ = dihedral angle
Closed cylinder r = radius of the circular base, h = height of the cylinder
Lateral surface area of a cone s = slant height of the cone,

r = radius of the circular base,
h = height of the cone

Full surface area of a cone s = slant height of the cone,

r = radius of the circular base,
h = height of the cone

Pyramid B = area of base, P = perimeter of base, L = slant height

##  Reference:

• Wikipedia Surface Area