Math
Triangular Prism Calculator
Find the volume, surface area, and lateral area of a triangular prism. Pick equilateral, right, isosceles, or scalene cross sections.
Triangular prism dimensions
Volume
155.8846
- Triangle area
- 15.5885
- Triangle perimeter
- 18
- Lateral surface area
- 180
- Total surface area
- 211.1769
- Side a
- 6
- Side b
- 6
- Side c
- 6
- Prism length
- 10
Rectangular faces
- Face on side a
- 6 x 10
- Area: 60
- Face on side b
- 6 x 10
- Area: 60
- Face on side c
- 6 x 10
- Area: 60
Frequently Asked Questions about the Triangular Prism Calculator
What is a triangular prism?
A triangular prism is a 3D solid with two parallel, congruent triangular bases connected by three rectangular side faces. The triangle can be equilateral, right, isosceles, or scalene.
How do you calculate the volume of a triangular prism?
Multiply the area of the triangular base by the prism length: V = A_triangle x L. The base area depends on the triangle type, for example (sqrt(3)/4) x s^2 for an equilateral triangle or Heron's formula for a scalene one.
What is the total surface area formula?
Total surface area equals the lateral surface area plus the two triangular bases: SA = (perimeter of triangle x L) + 2 x A_triangle. The lateral piece is just the three rectangular side faces added together.
How is Heron's formula used for the scalene case?
For sides a, b, c, compute the semi-perimeter s = (a + b + c) / 2, then area = sqrt(s x (s - a) x (s - b) x (s - c)). The calculator first checks the triangle inequality and rejects degenerate inputs.
Why does the calculator say my sides are invalid?
Every side and the prism length must be positive, and the three sides must satisfy the triangle inequality (a + b > c, a + c > b, b + c > a). For isosceles inputs, twice the equal side must exceed the base, otherwise the triangle collapses to a line.