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
| Field | What to enter |
|---|---|
| Triangle base given by | Choose one: Three sides, Two sides and the angle between them, Two angles and the side between them, Right triangle (two legs) |
| Side a | Units: cm, m, mm, in, ft, yd … |
| Side b | Units: cm, m, mm, in, ft, yd … |
| Side c | Units: cm, m, mm, in, ft, yd … |
| Angle γ (between a and b) | Units: °, rad, π rad, grad, turn |
| Angle β (at one end of a) | Units: °, rad, π rad, grad, turn |
| Angle γ (at the other end of a) | Units: °, rad, π rad, grad, turn |
| Prism length L | Units: 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) |
|---|---|
| 1.5 | 109.9608 |
| 2.25 | 121.282 |
| 3 | 132 |
| 3.75 | 142.2849 |
| 4.5 | 152.0985 |
| 6 | 169.8431 |
Formula
A = 2·A_base + (a + b + c)·L, A_base by Heron's formula
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.
Frequently asked questions
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.