# Surface Area of a Triangular Prism Calculator

URL: https://speedycalculator.com/calculators/math/surface-area-of-a-triangular-prism/
Last updated: 2026-10-30

> The surface area of a triangular prism calculator finds the total, lateral and base areas of a triangular prism from its triangle (three sides, two sides and an angle, two angles and a side, or two legs) and length.

## Inputs

- Triangle base given by
- Side a (cm, m, mm, in, ft, yd, km, mi)
- Side b (cm, m, mm, in, ft, yd, km, mi)
- Side c (cm, m, mm, in, ft, yd, km, mi)
- Angle γ (between a and b) (°, rad, π rad, grad, turn)
- Angle β (at one end of a) (°, rad, π rad, grad, turn)
- Angle γ (at the other end of a) (°, rad, π rad, grad, turn)
- Prism length L (cm, m, mm, in, ft, yd, km, mi)

## Results

- Triangle (base) area
- Lateral area
- Total surface area
- Volume

## Formula

```
A = 2·A_base + (a + b + c)·L,  A_base by Heron's formula
```

## Explanation

The surface area of a triangular prism tells you how much material makes a tent, a roof section or a gift box. It is two triangles plus three rectangles.

### How to use the Surface Area of a Triangular Prism Calculator

- **Triangle base given by**
- **Side a**
- **Side b**
- **Side c**
- **Angle γ (between a and b)**
- **Angle β (at one end of a)**
- **Angle γ (at the other end of a)**
- **Prism length L**

Results update as you type, and everything is calculated in your browser.

### How it works

Choose how the triangle is described, then enter the prism length L.

### Inputs explained

FieldWhat to enterTriangle base given byChoose one: Three sides, Two sides and the angle between them, Two angles and the side between them, Right triangle (two legs)Side aUnits: cm, m, mm, in, ft, yd …Side bUnits: cm, m, mm, in, ft, yd …Side cUnits: cm, m, mm, in, ft, yd …Angle γ (between a and b)Units: °, rad, π rad, grad, turnAngle β (at one end of a)Units: °, rad, π rad, grad, turnAngle γ (at the other end of a)Units: °, rad, π rad, grad, turnPrism length LUnits: cm, m, mm, in, ft, yd …

### What each result means

- **Triangle (base) area** = sqrt(([a] + [b] + [c])×(-[a] + [b] + [c])×([a] - [b] + [c])×([a] + [b] - [c]))÷4
- **Lateral area** = ([a] + [b] + [c])×[Prism length L]
- **Total surface area** = 2×[Triangle (base) area] + ([a] + [b] + [c])×[Prism length L]
- **Volume** = [Triangle (base) area]×[Prism length L]

### Example values

How the main result changes when **Side a** changes and everything else stays at the example values above:

Side a (cm)Total surface area (cm²)1.5109.96082.25121.28231323.75142.28494.5152.09856169.8431

## Worked example

Inputs — Triangle base given by: Three sides; Side a: 3 cm; Side b: 4 cm; Side c: 5 cm; Prism length L: 10 cm.

Results — Triangle (base) area = 6 cm²; Lateral area = 120 cm²; **Total surface area = 132 cm²**; Volume = 60 cm³.

## Key terms

- **Lateral area**: The area of the side faces.

## FAQ

**What is the lateral area?**
The three rectangular faces: perimeter of the triangle × length.

**Why two base areas?**
The prism has a triangle at each end.

**How do I use Heron's formula?**
s = (a + b + c)/2, area = √(s(s − a)(s − b)(s − c)).

**Does a right triangle make it easier?**
Yes – the base area is just half the product of the legs.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Solid geometry](https://mathworld.wolfram.com/SolidGeometry.html)