Rectangular prism: Difference between revisions
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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 (geometry) | 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, <math>V = lwh</math>. | The [[volume]] can be determined by multiplying the length, width, and height, <math>V = lwh</math>. | ||
The length of the interior [[diagonal]]s can be determined by using the formula <math>d = \sqrt{l^2 + w^2 + h^2}</math>. | 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 <math>v</math>. 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== | ||
Latest revision as of 20:07, 23 October 2025
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 
. Then we use the pythagorean theorem again to get
- The surface area of the prism is
See also
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