# Difference between revisions of "Rectangular prism"

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A '''rectangular prism''' (also '''cuboid''', '''rectangular box''', '''right rectangular prism''', '''rectangular paralleliped''') is a [[3D|three dimensional]] figure with 6 [[face]]s that are all [[rectangle]]s. | A '''rectangular prism''' (also '''cuboid''', '''rectangular box''', '''right rectangular prism''', '''rectangular paralleliped''') is a [[3D|three dimensional]] figure with 6 [[face]]s that are all [[rectangle]]s. | ||

− | Opposite faces of a rectangular prism are [[congruent]] and [[parallel]]. | + | Opposite faces of a rectangular [[prism]] are [[congruent (geometry) | congruent]] and [[parallel]]. |

− | The [[volume]] can be determined by multiplying the length, width, and height | + | The [[volume]] can be determined by multiplying the length, width, and height, <math>V = lwh</math>. |

− | The length of | + | The length of the interior [[diagonal]]s can be determined by using the formula <math>d = \sqrt{l^2 + w^2 + h^2}</math>. |

+ | |||

+ | Proof: To get a base diagonal, we use the [[pythagorean theorem]]: <math> \sqrt{l^2+w^2}</math>. We call that v. Then we use the pythagorean theorem again to get | ||

+ | * <math>diagonal=\sqrt{v^2+h^2}=\sqrt{l^2+w^2+h^2}</math> | ||

+ | |||

+ | |||

+ | |||

+ | * The [[surface area]] of the prism is <math>2lw+2wh+2lh</math> | ||

==See also== | ==See also== | ||

− | *[[Cube]] | + | *[[Cube (geometry) | Cube]] |

{{stub}} | {{stub}} |

## Latest revision as of 09:04, 12 September 2007

A **rectangular prism** (also **cuboid**, **rectangular box**, **right rectangular prism**, **rectangular paralleliped**) is a three dimensional figure with 6 faces that are all rectangles.

Opposite faces of a rectangular prism are congruent and parallel.

The volume can be determined by multiplying the length, width, and height, .

The length of the interior diagonals can be determined by using the formula .

Proof: To get a base diagonal, we use the pythagorean theorem: . We call that v. Then we use the pythagorean theorem again to get

- The surface area of the prism is

## See also

*This article is a stub. Help us out by expanding it.*