The surface area of a shape is the total area of all of the shape's faces. It can be considered the total extent of all of the shape's 2-subfacets in 2-dimensional space. The surface area of a polygon is typically just called its area. A surface area has dimensions of [length]2.
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| - The surface area of a shape is the total area of all of the shape's faces. It can be considered the total extent of all of the shape's 2-subfacets in 2-dimensional space. The surface area of a polygon is typically just called its area. A surface area has dimensions of [length]2.
- Surface area is how much exposed area an object has. It is expressed in square units. If an object has flat faces, its surface area can be calculated by adding together the areas of its faces. Even objects with smooth surfaces, such as spheres,
- 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.
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| abstract
| - The surface area of a shape is the total area of all of the shape's faces. It can be considered the total extent of all of the shape's 2-subfacets in 2-dimensional space. The surface area of a polygon is typically just called its area. A surface area has dimensions of [length]2.
- Surface area is how much exposed area an object has. It is expressed in square units. If an object has flat faces, its surface area can be calculated by adding together the areas of its faces. Even objects with smooth surfaces, such as spheres,
- 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. 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.
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