Volume of a prism represents the amount of three-dimensional space it occupies, measured in cubic units, and is calculated as , where is the area of a base and is the perpendicular distance between congruent bases. The understanding includes rectangular, triangular, and other prisms whose base areas can be found from familiar formulas, including by decomposition, while excluding oblique prisms and more advanced generalized treatments.
A prism has two matching, parallel bases. To find its volume, use
where:
The volume is measured in cubic units.
Example: Find the volume of a triangular prism with a triangular base that has a base of cm and a height of cm. The prism is cm long.
Find the area of the triangular base.
Use the triangle area formula:
Substitute the measurements:
Use the prism volume formula.
The distance between the triangular bases is cm:
Therefore, the volume of the triangular prism is
Remember to find the area of one base first, then multiply by the perpendicular distance between the bases.
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