Surface Area of a Triangular Prism Calculator
Total up all five faces of a right triangular prism — two triangular ends plus three rectangles. Enter the three sides of the triangle and the prism length in any one unit; the triangle area comes from Heron's formula, so no height measurement is needed.
Example: with Triangle side a 3 · Triangle side b 4 · Triangle side c 5 · Prism length (L) 10 → Total surface area: 132 square units.
- Triangle end area (Heron)6 square units each end
- Lateral area (a+b+c) × L120 square units
- Volume (bonus)60 cubic units
Computed by the calculator below using its default values. Change any input to see your own numbers.
SA = 2 × triangle area + perimeter × length. Heron's formula finds the triangle area from the three sides alone.
Two triangles and a wrap
A right triangular prism has exactly five faces: the two identical triangular ends and three rectangles wrapping around the sides. Each rectangle is one triangle side long and one prism-length wide, so the three of them together contribute (a + b + c) × L — the triangle's perimeter times the length. Add the two ends and you get SA = 2A + (a + b + c)L.
The clever part is getting the triangle area A without measuring a height. Heron's formula needs only the three sides: compute the semi-perimeter s = (a+b+c)/2, then A = √(s(s−a)(s−b)(s−c)). For the classic 3-4-5 right triangle, s = 6 and A = √(6·3·2·1) = 6. With a 10-unit length, that prism needs 2(6) + 12(10) = 132 square units of material — the number you would use to size sheet metal, tent fabric, or paint.
How it’s calculated
SA = 2A + (a + b + c) × L. Triangle area from Heron's formula: s = (a+b+c)/2, A = √(s(s−a)(s−b)(s−c)). Lateral area = perimeter × length (valid for right prisms, where the rectangles meet the ends at 90°). Bonus volume = A × L. Inputs failing the triangle inequality are rejected.
Right prisms only — ends perpendicular to the length. An oblique (slanted) prism has the same volume but larger lateral faces.
Worked examples
| Triangle sides | Length | End area | Total surface area |
|---|---|---|---|
| 3, 4, 5 | 10 | 6 | 132 |
| 6, 8, 10 | 12 | 24 | 336 |
| 5, 5, 6 | 8 | 12 | 152 |
| 4, 4, 4 (equilateral) | 10 | 6.93 | 133.86 |
| 5, 12, 13 | 20 | 30 | 660 |
Computed with Heron's formula and SA = 2A + (a+b+c)L; equilateral end area (√3/4)·16 ≈ 6.93.
Common mistakes
- Counting the triangle end once instead of twice — the prism has two identical ends.
- Using triangle sides that violate the triangle inequality (like 2, 3, 7); no such prism exists, and this page flags it.
- Mixing up surface area and volume: material to cover the prism is 2A + PL in square units; what fits inside is A × L in cubic units.
- Measuring the prism length along a slanted edge on an oblique prism — the perimeter × length shortcut only holds for right prisms.
Frequently asked questions
What is the surface area formula for a triangular prism?
SA = 2A + (a + b + c) × L, where A is the area of the triangular end and a, b, c are its sides. The first term covers both ends; the second is the three rectangular sides.
How do I find the triangle area without a height?
Heron's formula: with s = (a+b+c)/2, A = √(s(s−a)(s−b)(s−c)). For sides 3, 4, 5 that gives √(6×3×2×1) = 6, no height measurement required.
What counts as the prism length?
The distance between the two triangular ends, measured perpendicular to them. On a tent shape it is the ridge length; on an extruded beam it is the extrusion length.
Why does my 2, 3, 7 triangle return an error?
Those sides cannot close into a triangle — each side must be shorter than the sum of the other two. Re-measure; a transposed digit is the usual culprit.