If you ever wondered how to find the volume of a triangular prism, this triangular prism calculator is the thing you are looking for. Not only can it calculate the volume but also may be helpful if you need to determine the triangular prism surface area. Choose the option which fits your needs and experiment with the tool! If you are curious about triangular prism formulas behind the calculator, scroll down to find out more.

Triangular prism - what's that?

What is a prism? It's a solid object with:

  • identical two bases
  • three rectangular faces (right prism) or in parallelogram shape (oblique prism)
  • the same cross section along its whole length

We are using the term triangular prism to describe the right triangular prism, what is quite a common practice. If you are looking for other prism type, check our rectangular prism calculator.

Triangular prism formulas

Usually what you need to calculate are the triangular prism volume and its surface area. The two most basic equations are:

  • volume = 0.5 * b * h * length, where b is the length of the base of the triangle, h is the height of the triangle and length is prism length

  • area = length * (a + b + c) + (2 * base_area), where a, b, c are sides of the triangle and base_area is the triangular base area

But what if we don't have the height and base of the triangle? And how to find triangular prism surface area without all sides of the triangular base? Check out the other triangular prism formulas!

Triangular prism volume

In the triangular prism calculator you can easily find out the volume of that solid. A general formula is volume = length * base_area; the one parameter you always need to have given is the prism length, and there are four ways to calculate the base - triangle area. Our triangular prism calculator has all of them implemented, isn't it awesome?

The specific formulas look as follows:

  • Length * Triangular base area given triangle base and height

    It's this well-known formula mentioned before:

    volume = length * 0.5 * b * h

  • Length * Triangular base area given three sides (SSS)

    If you know the lengths of all sides, use the Heron's formula to find the area of triangular base:

    volume = length * 0.25 * √( (a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c) )

  • Length * Triangular base area given two sides and the angle between them (SAS)

    You can calculate area of a triangle easily from trigonometry:

    volume = length * 0.5 * a * b * sin(γ)

  • Length * Triangular base area given two angles and a side between them (ASA)

    You can calculate that using trigonometry:

    volume = = length * a² * sin(β) * sin(γ) / (2 * sin(β + γ))

Triangular prism surface area

If you want to calculate the surface area of the solid, the most well-known formula is the one given three sides of the triangular base :

  • area = length * (a + b + c) + (2 * base_area) = length * base_perimeter + (2 * base_area)

However, we don't always have the three sides given. What then?

  • Triangular base: given two sides and the angle between them (SAS)

    Using law of cosines, we can find the third triangle side:

    area = length * (a + b + √( b² + a² - (2 * b * a * cos(angle)))) + a * b * sin(angle)

  • Triangular base: given two angles and a side between them (ASA)

    Using law of sines, we can find the two sides of triangular base:

    area = (length * (a + a * (sin(angle1) / sin(angle1+angle2)) + a * (sin(angle2) / sin(angle1+angle2)))) + a * ((a * sin(angle1)) / sin(angle1 + angle2)) * sin(angle2)

The only option when you can't calculate triangular prism volume is having given triangle base and its height (do you know why? Think about it for a moment). All the other versions may be calculated with our triangular prism calculator.

How to find the volume of a triangular prism with this tool?

Let's check what's the volume and surface area of a tent shaped like a triangular prism:

  1. Find out what's the length of the triangular prism. Assume it's equal to 80 in, type this value into the first box of triangular prism calculator.
  2. Choose the option with your parameters given. For example, given three sides of our base.
  3. Enter base sides. Our tent has a = 60 in, b = 50 in and c = 50 in.
  4. Triangular prism surface area and volume appear in no time. It's 96,000 cu in (55.56 cu ft) and 15,200 in² (105.56 ft²).
Hanna Pamuła, PhD student

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