# Surface and area

Surface are two related concepts. The surface designates an extension or the area of a territory, it is what only has length and width while the area is a concept that allows assigning a measure to a surface.

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## Surface

The term is used to designate in geography the extension or area of territory while in mathematics it defines what only has length and width.

For mathematics, a surface is a set of points in Euclidean space that form a two-dimensional space.

## Area

It is a metric concept that assigns a measure to the extent of a surface. It is expressed in mathematics as surface units. It is a metric concept that requires the specification of a measure of length.

You can calculate the area of curved surfaces with differential geometry methods.

The area is the measure of the size of a region enclosed by a geometric figure. The area is an ancient concept that arose with the Egyptians, who had to calculate the area of their agricultural plots to reestablish their limits after the floods of the Nile.

To calculate the area of a polygon the area of all the triangles that make it up is added, this method was proposed by the Greek sage Antiphon around 430 BC. C. From this method, it is derived that any flat surface with straight sides or polygon can be triangulated allowing its area to be calculated.

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## Differences between Surface and Area

Sometimes they are used as synonyms, but they are concepts that complement each other and that should be used when there is no confusion between the geometric concept and its magnitude.

- Surfaces are a geometric concept that defines a set of tangent points that occupy a two-dimensional space.
- The area is the metric quantity associated with the geometric concept.