Triangular Prism Volume Calculator
A triangular prism with a base edge of 6, a triangle height of 4, and a prism length of 10 has a volume of 120 cubic units. This calculator finds the volume of a triangular prism from three measurements: the base edge of the triangle, the height of the triangle measured perpendicular to the base, and the length of the prism, the distance between the two triangular faces. A triangular prism is one of the most common three-dimensional shapes in textbooks and on tests. It shows up as a tent shape, a wedge, or a ramp in word problems. The volume formula follows the same pattern as every other prism: find the area of one face, the triangle, and multiply by how far that face extends in the third dimension, the prism length. The only tricky part is making sure you measure the triangle height perpendicular to the base edge, not along a slanted side. If you use a slanted side length instead of the perpendicular height, the area and volume will both be wrong.
Quick answer
The volume of a triangular prism is the area of the triangular base multiplied by the prism length.
Volume
120
Base area
12
What this tells you
- •The volume of a triangular prism is the area of the triangular base multiplied by the prism length.
- •The triangular base area uses the standard triangle formula: one half times base edge times triangle height.
- •All three measurements must be positive and use the same unit.
- •The result is in cubic units of whatever unit was used for the inputs.
How to Use
- 1Enter the base edge of the triangle, the length of the bottom side of the triangular face.
- 2Enter the triangle height, measured perpendicular from the base edge to the opposite vertex of the triangle.
- 3Enter the prism length, the distance between the two identical triangular faces.
- 4Read the volume and the base area. The volume is always base area times prism length.
How It Works
Formula
volume = (1/2 x base edge x triangle height) x prism lengthStart with the area of the triangular base using the standard triangle formula, one half times base times height. Then multiply that area by the prism length, the distance between the two triangular faces, to get the total volume. For a base edge of 6, a triangle height of 4, and a prism length of 10, the area is one half times 6 times 4 equals 12, and the volume is 12 times 10 equals 120 cubic units.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Standard triangular prism
Base area = 1/2 x 6 x 4 = 12. Multiply by the length of 10 to get 120.
Long narrow prism
Base area = 1/2 x 3 x 2 = 3. Multiply by 15 to get 45.
Typical classroom example
Base area = 1/2 x 5 x 8 = 20. Multiply by 12 to get 240.
Common Triangular Prism Volumes
| Base | Tri. Height | Length | Volume |
|---|---|---|---|
| 6 | 4 | 10 | 120 |
| 5 | 8 | 12 | 240 |
| 3 | 2 | 15 | 45 |
| 8 | 6 | 20 | 480 |
Common mistakes
- Confusing the triangle height with the prism length. The triangle height is measured on the triangular face, while the prism length is the distance between the two triangular faces.
- Using slant side length instead of the perpendicular height inside the triangle.
- Forgetting to divide by 2 when calculating the triangular base area.
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