Quick answer: the volume of a triangular prism is V = ½ × b × h × l — the triangle's area (half of base × height) multiplied by the prism's length. With a 4 × 3 triangle extended 10 units: ½ × 4 × 3 × 10 = 60 cubic units.
The triangular prism formula, step by step
where b = triangle base · h = triangle height (perpendicular to b) · l = prism length
Like every prism, this is just cross-section area × length. The cross-section happens to be a triangle, so its area is ½bh:
- Triangle area: ½ × 4 × 3 = 6 square units
- Extrude along the length: 6 × 10 = 60 cubic units
Any triangle works — right, isosceles, scalene — as long as h is measured perpendicular to the base you chose, not along a sloped side. If all you have is the three side lengths, get the area from Heron's formula first (see the FAQ), then multiply by the length.
Common triangular-prism objects — quick reference
| Object | Triangle (b × h) | Length | Volume |
|---|---|---|---|
| Wheelchair ramp wedge | 6 ft run × 0.5 ft rise | 3 ft wide | 4.5 ft³ |
| V-shaped water trough | 2 ft top × 1.5 ft deep | 8 ft | 12 ft³ ≈ 90 gal |
| Camping tent (A-frame) | 5 ft wide × 4 ft tall | 7 ft | 70 ft³ |
| Gable attic space | 24 ft span × 6 ft rise | 40 ft | 2,880 ft³ |
| Toblerone bar (100 g) | ~3 cm × 2.6 cm | ~21 cm | ≈ 82 cm³ |
Where triangular prism volume shows up in real life
Concrete ramps and wedges
A loading-dock ramp 12 ft long rising 2 ft, poured 6 ft wide, is a triangular prism on its side: ½ × 12 × 2 × 6 = 72 ft³ ≈ 2.67 cubic yards of concrete. The concrete volume calculator turns that into bag counts and adds a waste margin.
Attic and roof space
The space under a gable roof is a triangular prism lying on the ceiling joists: span × rise ÷ 2 × house length. A 28-ft-wide house with a 7-ft ridge rise, 44 ft long: ½ × 28 × 7 × 44 = 4,312 ft³ — the number that sizes attic ventilation fans (most codes want an air change rate based on exactly this volume).
Drainage channels
V-shaped roadside swales carry water in a triangular cross-section. One 3 ft across the top and 1 ft deep, running 200 ft, holds ½ × 3 × 1 × 200 = 300 ft³ ≈ 2,244 gallons when brimful. Flat-bottomed ditches are trapezoids — use the trapezoidal prism calculator for those.
Common mistakes & pro tips
- Sloped side used as triangle height. The h in ½bh must meet the base at 90°. In a right triangle the two legs are base and height; in others, drop a perpendicular.
- Triangle height and prism length swapped. The result is the same number only when they happen to be equal. Check the diagram: h is on the triangular face, l runs between the two faces.
- Halving twice. ½bh already accounts for the triangle. Don't halve the final volume again.
- Pro tip — sloped-site slabs. A slab poured on a slope has a triangular wedge on top of the rectangular section. Compute the box and the wedge separately, then add.
How to use this calculator
- Measure the triangle. Measure the triangular end's base b and its perpendicular height h — the straight-line distance from the base to the opposite corner, not along a sloped side.
- Measure the prism length. Measure how far the triangle extends — the length l between the two triangular ends.
- Let it apply V = ½ b h l. Half of base times height gives the triangle's area; multiplying by the length extrudes it into a volume.
- Convert the result. Switch between cubic units, liters and gallons in the output menu.
Frequently asked questions
What is the formula for the volume of a triangular prism?
V = ½ × b × h × l — half the triangle's base times its height (that's the triangle's area) times the prism's length. A prism with a 4 cm base, 3 cm triangle height and 10 cm length holds ½ × 4 × 3 × 10 = 60 cm³.
Which height do I use — the triangle's or the prism's?
The formula uses the triangle's height: the perpendicular distance from the triangle's base to its opposite vertex. The third measurement is the prism's length — how far the triangular cross-section extends. Mixing these up is the most common error with this shape.
How do I find the volume if I know the three sides of the triangle?
Use Heron's formula for the triangle's area: with s = (a+b+c)/2, area = √(s(s−a)(s−b)(s−c)); then multiply by the prism length. A 3-4-5 triangle has s = 6 and area = √(6×3×2×1) = 6, so a 10-unit-long prism holds 60 cubic units.
How much water does a triangular trough hold?
A V-shaped trough is an inverted triangular prism. One 2 ft wide at the top, 1.5 ft deep and 8 ft long holds ½ × 2 × 1.5 × 8 = 12 ft³ ≈ 90 US gallons.