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Volume of a Prism: Triangular, Pentagonal + Examples
Published: 12.08.2026·Updated: 14.08.2026
Nadia Rahmawati
Math Curriculum Team, Algonova
A prism is a solid with two parallel faces identical in shape and size, joined by rectangular side faces. Those two parallel faces are the base and the top. It is taught in Year 8 as part of flat-faced solids.
One Formula for Every Prism
That is all — and it holds for every prism without exception: triangular, pentagonal, hexagonal, even cuboids and cylinders.
Why? Because a prism is essentially its base "stacked" to a height of h. A base of 20 cm² stacked 5 cm high is five layers of 20 cm² each.
| Type of prism | Base area | Volume |
|---|---|---|
| Triangular prism | ½ × b × h₆ | ½ × b × h₆ × h |
| Rectangular prism (cuboid) | l × w | l × w × h |
| Pentagonal prism | area of pentagon | area of pentagon × h |
| Cylinder (circular prism) | πr² | πr² × h |
A child who sees this table stops memorising four separate formulas. The cuboid and cylinder formulas are not new — both are special cases of the same one.
Two Different Heights
🔴 This is the number one source of error in the topic. A triangular prism has two heights:
- Base height (h₆) — the height of the triangle forming the base, used to find the base area
- Prism height (h) — the distance between base and top, used in the volume formula
Exam questions almost always give different values for each, and swapping them once makes the whole answer wrong. How to tell them apart: the prism height is the one connecting the two parallel faces; the base height lives inside the triangle.
Worked Examples
Example 1 — triangular prism. The base triangle has base 6 cm and height 4 cm. The prism is 10 cm tall.
- Base area = ½ × 6 × 4 = 12 cm²
- Volume = 12 × 10 = 120 cm³
Example 2 — right-angled triangular prism. The perpendicular sides are 3 cm and 4 cm, prism height 12 cm.
- Base area = ½ × 3 × 4 = 6 cm²
- Volume = 6 × 12 = 72 cm³
Example 3 — finding the height. A prism has volume 240 cm³ and base area 30 cm². What is its height?
- h = 240 ÷ 30 = 8 cm
Surface Area of a Prism
The first part is the base and top; the second is all the side faces, which unroll into one large rectangle.
The Mistakes That Actually Cost Marks
1. Swapping base height and prism height. The number one cause. Questions supply both numbers deliberately.
2. Forgetting the half in the triangle's area. The answer comes out exactly double — an instantly recognisable pattern.
3. Wrong units. Volume is always cubic (cm³), area always square (cm²). See units of area.
4. Assuming each prism type has its own formula. All of them are base area times height.
5. Mixing units. If the base is in cm and the height in m, convert first.
