# How big is my triangular prism?

Finds the volume, base area, lateral area and total surface area of a triangular prism from the three sides of its base, a base and height, or the legs of a right triangle, and its length.

- Page: https://www.acalculator.org/math/triangular-prism-calculator
- JSON spec: https://www.acalculator.org/math/triangular-prism-calculator.json
- Version: 61d8c361ecce

## Default answer

Example with the default inputs (Triangle known by Three sides, Side a 3, Side b (base) 4, Side c 5, Prism length 10): A triangular prism 10 long with a base area of 6 has a volume of 60.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| by | Triangle known by | How you know the triangular base: its three sides, a base and height, or the legs of a right triangle. |
| a | Side a | One side of the triangle (a leg, for a right triangle). |
| b | Side b (base) | The base side of the triangle (the other leg, for a right triangle). |
| c | Side c | The third side of the triangle. |
| h | Triangle height | The height of the triangle, at right angles to side b. |
| l | Prism length | The length of the prism: the distance between its two triangular ends. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| volume | Volume | Base area × prism length, in cubic units. |
| baseArea | Base area | The area of one triangular end, in square units. |
| perimeter | Base perimeter | a + b + c, the distance around the triangle. |
| lateral | Lateral area | The three rectangular faces: perimeter × prism length. |
| surface | Total surface area | Two triangular ends plus the lateral area: 2 × base area + perimeter × length. |
| hypotenuse | Hypotenuse | The long side of a right triangle: √(a² + b²). |

## Method

V = B × L; SA = 2B + (a + b + c) × L. B = √(s(s − a)(s − b)(s − c)) with s = (a + b + c) ÷ 2 (three sides), B = ½ × b × h (base and height), or B = ½ × a × b with c = √(a² + b²) (right triangle).

## Assumptions

- The prism is a right prism: the rectangular faces are at right angles to the two equal triangular ends.
- All lengths are in the same unit; areas come out in that unit squared and the volume in that unit cubed.
- With a base and height only, the other two sides are unknown, so the page gives the volume and base area but not the surface area.

## Worked examples

1. by = base, b = 12, h = 6, l = 10 gives baseArea = 36, volume = 360. Source: OpenStax, Contemporary Mathematics, §10.7 Volume and Surface Area (right prism: V = B × h, SA = 2B + ph), https://openstax.org/books/contemporary-mathematics/pages/10-7-volume-and-surface-area (Example 10.57: base area ½ × 12 × 6 = 36 in²).
2. by = sides, a = 10, b = 15, c = 7, l = 20 gives baseArea = 29.393877, volume = 587.877538, perimeter = 32, lateral = 640. Source: OpenStax, Algebra and Trigonometry 2e, §10.2 Non-right Triangles: Law of Cosines (Heron’s formula), https://openstax.org/books/algebra-and-trigonometry-2e/pages/10-2-non-right-triangles-law-of-cosines (s = 16, area = √(16 × 6 × 1 × 9) ≈ 29.4); OpenStax, Contemporary Mathematics, §10.7 Volume and Surface Area (right prism: V = B × h, SA = 2B + ph), https://openstax.org/books/contemporary-mathematics/pages/10-7-volume-and-surface-area.
3. by = right, a = 3, b = 4, l = 10 gives hypotenuse = 5, baseArea = 6, volume = 60, perimeter = 12, lateral = 120, surface = 132. Source: OpenStax, Contemporary Mathematics, §10.7 Volume and Surface Area (right prism: V = B × h, SA = 2B + ph), https://openstax.org/books/contemporary-mathematics/pages/10-7-volume-and-surface-area.
4. by = sides, a = 2.5, b = 2.5, c = 2.5, l = 4 gives baseArea = 2.706329, volume = 10.825318, surface = 35.412659. Source: OpenStax, Algebra and Trigonometry 2e, §10.2 Non-right Triangles: Law of Cosines (Heron’s formula), https://openstax.org/books/algebra-and-trigonometry-2e/pages/10-2-non-right-triangles-law-of-cosines; OpenStax, Contemporary Mathematics, §10.7 Volume and Surface Area (right prism: V = B × h, SA = 2B + ph), https://openstax.org/books/contemporary-mathematics/pages/10-7-volume-and-surface-area.

## FAQ

### How do I find the volume of a triangular prism?

Find the area of the triangle at one end, then multiply by the length of the prism. A triangle with base 12 in and height 6 in has an area of ½ × 12 × 6 = 36 in², so a prism 10 in long holds 36 × 10 = 360 in³.

### How do I find the surface area of a triangular prism?

Add the two triangular ends and the three rectangles: SA = 2B + (a + b + c) × L. For a 3-4-5 right triangle and a length of 10, that is 2 × 6 + 12 × 10 = 132 square units.

### What if I only know the three sides of the triangle?

Use Heron’s formula. Let s = (a + b + c) ÷ 2; then the area is √(s(s − a)(s − b)(s − c)). For sides 10, 15 and 7, s = 16 and the area is √864 ≈ 29.39.

### Why is there no surface area in the base and height mode?

A base and a height fix the area of the triangle, but not the lengths of its other two sides, and the rectangles on those sides need them. Use the three sides mode to get the surface area.

### What units does the calculator use?

Any unit you like, as long as every length uses the same one. The areas come out in that unit squared and the volume in that unit cubed: inches give in² and in³, centimetres give cm² and cm³.

### What is the difference between the length and the height?

The triangle height is measured inside the triangle, at right angles to its base side. The prism length is the distance between the two triangular ends. Some books call the prism length its height.

## Sources

- OpenStax, Contemporary Mathematics, §10.7 Volume and Surface Area: right prism SA = 2B + ph and V = B·h; Example 10.57 (triangle base 12 in, height 6 in, length 10 in). https://openstax.org/books/contemporary-mathematics/pages/10-7-volume-and-surface-area (retrieved 2026-10-01)
- OpenStax, Algebra and Trigonometry 2e, §10.2 Non-right Triangles: Law of Cosines, Heron’s formula and its example with sides 10, 15 and 7. https://openstax.org/books/algebra-and-trigonometry-2e/pages/10-2-non-right-triangles-law-of-cosines (retrieved 2026-10-01)