# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# Area

Area[reg]
gives the area of the two-dimensional region reg.

Area[{x1,,xn},{s,smin,smax},{t,tmin,tmax}]
gives the area of the parametrized surface whose Cartesian coordinates are functions of s and t.

Area[{x1,,xn},{s,smin,smax},{t,tmin,tmax},chart]
interprets the as coordinates in the specified coordinate chart.

## Details and OptionsDetails and Options

• Area is also known as surface area.
• A two-dimensional region can be embedded in any dimension greater than or equal to two.
• In Area[x,{s,smin,smax},{t,tmin,tmax}], if x is a scalar, Area returns the area of the parametric surface .
• Coordinate charts in the fourth argument of Area can be specified as triples in the same way as in the first argument of CoordinateChartData. The short form in which dim is omitted may be used.
• The following options can be given:
•  Assumptions \$Assumptions assumptions to make about parameters Method Automatic method to use
• Specific methods include:
•  Automatic automatic method selection "Integrate" exact symbolic integration "NIntegrate" numeric integration
• Additional method suboptions can be given in the form Method->{,opts}.
• Any option of Integrate or NIntegrate can be passed as a method suboption to the corresponding method.
• Symbolic limits of integration are assumed to be real and ordered. Symbolic coordinate chart parameters are assumed to be in range given by the property of CoordinateChartData.

## ExamplesExamplesopen allclose all

### Basic Examples  (5)Basic Examples  (5)

The area of a disk:

 Out[1]=

The surface area of a sphere:

 Out[1]=

The area of an annulus with inner radius 1 and outer radius 2:

 Out[1]=

The surface area of the open cylinder , expressed in cylindrical coordinates:

 Out[1]=

The area of a region of dimension zero or one is :

 Out[1]=

The area of a region of dimension three or higher is :

 Out[2]=