Volume of a Triangular Prism Formula
What is the formula for the volume of a triangular prism?
Answer
Here a is the side (or base), h is the height, perpendicular to the base, l is the slant height of a face, or the length along the solid. The result comes out in cubic units.
Where the formula comes from
Base times length again, and the base is a triangle: ½·a·h of area repeated along a length l. Note that two different heights appear — h stands up inside the triangle, l runs along the prism.
Worked examples
Let a = 6, h = 4, l = 10. Then the volume of a triangular prism = 120 cubic units.
Let a = 3.5, h = 2, l = 7. Then the volume of a triangular prism = 24.5 cubic units.
The common mistake
Forgetting the ½ and treating the prism as a box. a·h·l is the rectangular prism built on the same rectangle; the triangular one is exactly half of it, so dropping the ½ doubles the answer. (Swapping h and l, by contrast, changes nothing — multiplication does not care about the order.)
Other quantities: Triangular prism
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See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
<a href="https://calculat.io/en/geometry/shape-formula/volume--triangular-prism">Volume of a Triangular Prism Formula - Calculatio</a>
Values from the Formula (h = 4, l = 10)
| If a = | Volume |
|---|---|
| 1 | 20 cubic units |
| 2 | 40 cubic units |
| 3 | 60 cubic units |
| 4 | 80 cubic units |
| 5 | 100 cubic units |
| 10 | 200 cubic units |