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The surface area of a solid object is a measure of the total area that the surface of the object occupies. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces.
This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration. 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.