The Area of a Surface is the amount of material needed to ``cover'' it completely. The Area of a Triangle is
given by

(1) |

(2) |

(3) |

(4) |

(5) |

Calculus and, in particular, the Integral, are powerful tools for computing the Area between a curve
and the *x*-Axis over an Interval , giving

(6) |

(7) |

(8) | |||

(9) |

For the Area of special surfaces or regions, see the entry for that region. The generalization of Area to 3-D is called Volume, and to higher Dimensions is called Content.

**References**

Gray, A. ``The Intuitive Idea of Area on a Surface.'' §13.2 in *Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, pp. 259-260, 1993.

© 1996-9

1999-05-25