Volume of a Triangular Prism Formula

Geometry Formulas: Area, Volume, Perimeter
Formula:

What is the formula for the volume of a triangular prism?

Answer

Volume of a triangular prism
V = ½ · a · h · l

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

V = ½ · a · h · l

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

Related Calculations

See Also

Geometry Formulas: Area, Volume, Perimeter

These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the volume of a triangular prism? (The answer is: V = ½ · a · h · l). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Formula:

Values from the Formula (h = 4, l = 10)

If a =Volume
120 cubic units
240 cubic units
360 cubic units
480 cubic units
5100 cubic units
10200 cubic units

FAQ

What is the formula for the volume of a triangular prism?

Volume of a triangular prism V = ½ · a · h · l

Where does this formula come 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.

What is the most common mistake here?

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.)

How do I use this formula?

Put your own numbers in place of the letters. With a = 3.5, h = 2, l = 7, for instance, the formula V = ½ · a · h · l gives = 24.5 cubic units.

See Also