Every prism and pyramid is built on a base shape, and the base tells you everything. A prism has two matching ends joined by rectangles. If its base has n sides, it has n + 2 faces, 3 × n edges and 2 × n vertices. A pyramid has one base and triangles that meet at a point. If its base has n sides, it has n + 1 faces, 2 × n edges and n + 1 vertices. So a hexagonal prism (base 6) has 8 faces, 18 edges and 12 vertices. You can also work backwards: a prism with 15 edges has 15 ÷ 3 = 5 sides on its base.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- prism
- a solid with two matching ends joined by rectangles
- pyramid
- a solid with one base and triangles that meet at a point
- base
- the face a prism or pyramid is named after
Worked examples
This is a triangular prism. How many edges does it have?
- 1.The base has 3 sides.
- 2.A prism has 3 × 3 = 9 edges: 3 on each end and 3 joining them.
= 9
An octagonal pyramid has a base with 8 sides. How many vertices does it have?
- 1.The base has 8 corners.
- 2.Add 1 for the point at the top: 8 + 1 = 9.
= 9
A prism has 18 edges. How many faces does it have?
- 1.18 ÷ 3 = 6, so the base has 6 sides.
- 2.A prism has 6 + 2 = 8 faces.
= 8
For parents
Method: Find the number of sides on the base, then use the prism or pyramid pattern.
What to say: How many sides does the base have? Is it a prism with two ends, or a pyramid with a point?
Common mistakes:
- Counts faces but misses a base: one end of a prism, or the base of a pyramid.
- Counts the edges round the base (and top) but forgets the edges running up the sides.
- Counts the corners of one base only: forgets the other end of a prism or the top point of a pyramid.
- Mixes up the words face, edge and vertex, giving the count of a different part (edges for faces, and so on).
- Uses the pyramid pattern for a prism or the prism pattern for a pyramid.
- Works back to the number of sides on the base correctly but gives that as the answer, missing the second step.