Triangular Prism Volume Calculator
Calculate the volume of a triangular prism using triangle base, triangle height, and prism length with our triangular prism volume calculator.
What Is a Triangular Prism?
A triangular prism is a three-dimensional solid with two parallel triangular faces connected by three rectangular faces. The two triangular ends are congruent and remain the same shape all along the prism length.
Common examples include wedge-shaped packaging, roof trusses, tent profiles, support blocks, and many architectural or mechanical parts with a constant triangular cross-section.
Volume of a Triangular Prism Formula
Formula Variables Explained:
The base edge of the triangular cross-section.
The perpendicular height of the triangular cross-section measured from the base.
The distance the triangular face extends to form the prism.
The volume of a triangular prism is found by multiplying the area of its triangular base by the prism length.
Because the area of a triangle is (1/2) × base × height, the full prism formula becomes V = (1/2) × b × h × L, where b is the triangle base, h is the triangle height, and L is the prism length.
How to find the volume of a Triangular Prism?
- 1Measure the triangle base b and the perpendicular triangle height h.
- 2Calculate the triangular base area using A = (1/2) × b × h.
- 3Measure the prism length L between the two triangular ends.
- 4Multiply the triangular area by the prism length to get the total volume.
- 5Express the result in cubic units such as cm³, m³, in³, or ft³.
Example: Calculate the Volume of a Triangular Prism
Example 1: Calculate the volume of a triangular prism with base 12 cm, height 8 cm, and length 20 cm
Problem: A triangular prism has a triangular cross-section with base 12 cm and perpendicular height 8 cm. Its prism length is 20 cm. Find the volume.
- Formula: V = (1/2) × b × h × L
- Triangle area = (1/2) × 12 × 8 = 48 cm²
- V = 48 × 20 = 960 cm³
Frequently Asked Questions (FAQ)
Q: Do I use the slanted side of the triangle in the formula?
No. Use the triangle base and its perpendicular height. A slanted side alone is not enough unless you first use it to find the perpendicular height.
Q: Why do I calculate the triangle area first?
A prism volume always equals cross-sectional area multiplied by length. For a triangular prism, the cross-section is a triangle, so you find its area first.
Q: Can any type of triangle be used in a triangular prism?
Yes. The triangle can be right, isosceles, scalene, or equilateral, as long as you know the correct base and perpendicular height for the triangular face.