Corbett Maths Volume of Triangular Prism

The Corbett Maths volume of a triangular prism resource gives you the formula and practice questions to work out the space inside a triangular prism. You enter the base length, base height, and prism length, and the calculator returns the volume in cubic units. This page explains the formula, shows a worked example, and covers the common mistakes and contexts where you’ll actually use it.

Formula

The volume of a triangular prism is the area of the triangular cross-section multiplied by the length of the prism. In words:

Volume = (½ × base × height of triangle) × length of prism

In symbols:

V = ½ × b × h × l

• V – volume (cubic units, e.g., cm³, m³, in³)
• b – base of the triangular face (same unit as h)
• h – perpendicular height of the triangular face (measured at a right angle to the base)
• l – length of the prism (the distance between the two triangular faces)

All three dimensions must be in the same unit before multiplying. If you mix cm and m, the result will be off by a factor of 100 or more.

Worked Example

Use the default values from the calculator: base length = 6 cm, base height = 4 cm, prism length = 10 cm.

1. Find the area of the triangular face: ½ × 6 × 4 = 12 cm².
2. Multiply by the prism length: 12 × 10 = 120 cm³.

The calculator gives 120.00 cm³, matching the step-by-step result. Note that the units are cubic because you multiplied three linear measurements.

When to Use This Formula

You will use this formula in geometry classes, in construction (e.g., concrete for a triangular channel), in packaging design, and in any situation where a solid has a constant triangular cross-section. The key is that the two triangular ends must be identical and parallel. If the shape tapers or the ends are different sizes, it is not a prism and this formula does not apply.

This is also a common question on GCSE maths papers in the UK, which is why the Corbett Maths resources are so widely searched. The formula appears in both foundation and higher tier exams, usually as a direct calculation or as part of a problem involving surface area.

How to Read the Result

The volume tells you how much space the prism occupies. A result of 120 cm³ means you could fit 120 one-centimetre cubes inside the shape. If you need the volume in litres, remember that 1 litre = 1000 cm³, so 120 cm³ = 0.12 litres. For larger prisms, 1 m³ = 1000 litres.

If you are working in inches or feet, the volume will be in cubic inches or cubic feet. To convert to gallons (US), use 1 US gallon = 231 in³; for UK gallons, use 1 UK gallon = 277.42 in³. Always check which gallon system your context uses.

Common Mistakes

• Using the wrong height: The height in the formula must be the perpendicular height of the triangle, not the slant height or a side length.
• Forgetting the ½: The area of a triangle is half base times height. A common error is to multiply base × height × length without halving.
• Mixing units: If the base is in cm and the length in m, convert one to the other first. For example, 10 cm = 0.1 m.
• Confusing prism length with triangle height: The prism length is the distance between the two triangular faces, not the height of the triangle.
• Rounding too early: If you round intermediate steps, the final answer can be noticeably off. Keep full precision until the last step.

Limits of the Formula

This formula only works for a right prism, where the two triangular faces are directly above each other and the sides are rectangles. If the prism is oblique (leaning to one side), the volume is still the cross-sectional area times the perpendicular length, but the length to use is the perpendicular distance between the faces, not the slanted edge. In most school problems, the prism is right, so the given length is correct.

Also, the triangle can be any type – right, isosceles, equilateral, or scalene – as long as you know the base and the perpendicular height. If you only know the three side lengths, you can find the area using Heron’s formula first, then multiply by the prism length.

Frequently Asked Questions

What is the formula for the volume of a triangular prism?

The formula is V = ½ × b × h × l, where b is the base of the triangle, h is the perpendicular height of the triangle, and l is the length of the prism. Multiply the triangle’s area by the prism’s length.

How do I find the volume of a triangular prism without the height?

You need the area of the triangular face. If you know all three sides, use Heron’s formula to get the area, then multiply by the prism length. If you know the base and two sides, you can find the height using the Pythagorean theorem if the triangle is right, or trigonometry for other cases.

What units does the volume come in?

The volume is in cubic units, matching the units of the three dimensions. For example, if you measure in cm, the volume is in cm³. If you measure in metres, it’s m³. You can convert to litres (1 L = 1000 cm³) or gallons if needed.

Why is there a half in the formula?

The half comes from the area of a triangle. A triangle is half of a rectangle with the same base and height. So the triangular face’s area is ½ × base × height, and then you multiply by the prism length to get the volume.

Does the type of triangle matter?

No, as long as you know the base and the perpendicular height. A right triangle, an equilateral triangle, or a scalene triangle all use the same formula. The key is that the height is measured perpendicular to the base.

How is this different from the volume of a rectangular prism?

A rectangular prism uses V = length × width × height because the base is a rectangle. A triangular prism uses half of that for the same base dimensions because a triangle is half of a rectangle. So for the same base and length, a triangular prism has half the volume of a rectangular prism.

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in b | Base length | cm | 6 | 0
in bh | Base height | cm | 4 | 0
in l | Prism length | cm | 10 | 0
out v | Volume | cm³ | 0.5 * b * bh * l | 2