Surface area Surface area The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which 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 surface area is based on methods
Surface area a certain class of surfaces that satisfies several natural requirements. The most fundamental property of the surface area is its additivity: "the area of the whole is the sum of the areas of the parts". More rigorously, if a surface "S" is a union of finitely many pieces "S", …, "S" which do not overlap except at their boundaries, then Surface areas of flat polygonal shapes must agree with their geometrically defined area. Since surface area is a geometric notion, areas of congruent surfaces must be the same and the area must depend only on the shape of the surface,