What this calculator does
The surface area of a triangular prism is the total area of material needed to cover every face: the two triangular ends plus the three rectangular sides running the length of the prism. It is the figure needed for cladding, painting or working out sheet material, as distinct from the volume the same shape can hold.
This calculator leads with that total surface area, taking the three sides of the triangular base and the prism length, and returning the total figure with the triangular ends and the rectangular side faces broken out separately underneath.
The formula
The triangular base area comes from Heron’s formula: with semiperimeter s = (a+b+c)/2, base area = √(s(s−a)(s−b)(s−c)). Total surface area then adds the two triangular ends, 2 × base area, to the three rectangular side faces, whose combined area is the base’s perimeter multiplied by the prism length.
| Term | Meaning |
|---|---|
| Base area | The area of the triangular cross-section at each end of the prism. |
| Perimeter × length | The combined area of the three rectangular side faces. |
| Prism length | The distance the triangular cross-section is extended to form the solid. |
The inputs explained
| Field | What to enter |
|---|---|
| Base side a | One side of the triangular base. |
| Base side b | A second side of the triangular base. |
| Base side c | The third side of the triangular base. |
| Prism length | The length the triangular cross-section is extended along to form the prism. |
When to use it
Cladding or painting a wedge-shaped structure
A tent, roof wedge or triangular duct needs its surface area, not its volume, to work out how much cladding, canvas or paint will cover every face.
Cutting sheet material for a triangular prism surface area formula problem
Given the three base sides and the length, this gives the total flat material needed before folding or assembling into the finished triangular prism shape.
Comparing material cost against a rectangular equivalent
A triangular prism and a rectangular prism covering a similar footprint can need noticeably different amounts of surface material, and comparing the two totals catches that before ordering stock.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does surface area change as a triangular prism gets longer?
A fixed right-angled triangular base of sides 3, 4 and 5, extended to a range of prism lengths.
| Prism length | Total surface area | Lateral (side-face) surface |
|---|---|---|
| 5 | 72.000 | 60.000 |
| 10 | 132.000 | 120.000 |
| 20 | 252.000 | 240.000 |
| 30 | 372.000 | 360.000 |
| 50 | 612.000 | 600.000 |
How does the base shape affect surface area at a fixed length?
The third side of the triangular base varying between the limits a valid triangle allows, at a fixed prism length of 10.
| Side c | Total surface area | Triangular cross-section area |
|---|---|---|
| 2 | 95.809 | 2.905 |
| 3 | 108.944 | 4.472 |
| 4 | 121.124 | 5.562 |
| 5 | 132.000 | 6.000 |
| 6.9 | 143.025 | 2.012 |
Questions
What is the formula for the surface area of a triangular prism?
Total surface area = 2 × base area + perimeter × length, where the base area comes from Heron’s formula applied to the three base sides, and the perimeter is those three sides added together.
What is the surface area of a triangular prism used for?
It gives the total area of material, sheet metal, canvas, cladding or paint, needed to cover every face of the solid: the two triangular ends and the three rectangular sides.
How is surface area of a rectangular prism different from a triangular one?
A rectangular prism’s surface area is 2(lw + lh + wh), from three rectangular pairs of faces. A triangular prism instead has two triangular ends plus three rectangular sides whose combined area depends on the triangular base’s perimeter rather than a second and third rectangle dimension.
Do I need the height of the triangle as well as its sides?
No. Heron’s formula finds the triangular base’s area directly from its three side lengths, so entering the three base sides and the prism length is enough for the full surface area.
For the volume of the same solid, see the triangular prism calculator. For a rectangular-based solid instead, see the rectangular prism and cube calculator.