**Surface area** is the total area of the faces and curved surface of the a solid figure. Mathematical description of the surface area is considerably more involved than the definition of arc length or 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.

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.

Read more about Surface Area: Definition of Surface Area, Common Formulas, In Chemistry, In Biology

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### Famous quotes containing the words area and/or surface:

“Now for civil service reform. Legislation must be prepared and executive rules and maxims. We must limit and narrow the *area* of patronage. We must diminish the evils of office-seeking. We must stop interference of federal officers with elections. We must be relieved of congressional dictation as to appointments.”

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“It was a pretty game, played on the smooth *surface* of the pond, a man against a loon.”

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