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 xi are functions of s and t.

Area[{x1,,xn},{s,smin,smax},{t,tmin,tmax},chart]

interprets the xi as coordinates in the specified coordinate chart.

Details 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 {s,t,x}.
  • Coordinate charts in the fourth argument of Area can be specified as triples {coordsys,metric,dim} 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:
  • AccuracyGoalInfinitydigits of absolute accurary sought
    Assumptions$Assumptionsassumptions to make about parameters
    GenerateConditionsAutomaticwhether to generate conditions on parameters
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PrecisionGoalAutomaticdigits of precision sought
    WorkingPrecisionInfinitythe precision used in internal computations
  • Symbolic limits of integration are assumed to be real and ordered. Symbolic coordinate chart parameters are assumed to be in range given by the "ParameterRangeAssumptions" property of CoordinateChartData.
  • Area can be used with symbolic regions in GeometricScene.

Examples

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Basic Examples  (4)

The area of a disk:

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The surface area of a sphere:

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

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

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Scope  (18)

Options  (3)

Applications  (4)

Properties & Relations  (5)

Possible Issues  (2)

Introduced in 2014
(10.0)
|
Updated in 2019
(12.0)