geometry · Year 5 · Suggested learning sequence
Prisms and pyramids
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.
Sample questions
This is a triangular prism. How many faces does it have?
- Start from the base: it has 3 sides.
- A prism has two 3-sided ends joined by 3 rectangles: 3 + 2 = 5 faces, 3 × 3 = 9 edges and 3 × 2 = 6 vertices.
- The triangular prism has 5 faces.
Answer: 5
This is a square pyramid. How many vertices does it have?
- Start from the base: it has 4 sides.
- A pyramid has one 4-sided base and 4 triangles meeting at the top: 4 + 1 = 5 faces, 4 × 2 = 8 edges and 4 + 1 = 5 vertices.
- The square pyramid has 5 vertices.
Answer: 5
This is a rectangular prism. How many edges does it have?
- Start from the base: it has 4 sides.
- A prism has two 4-sided ends joined by 4 rectangles: 4 + 2 = 6 faces, 4 × 3 = 12 edges and 4 × 2 = 8 vertices.
- The rectangular prism has 12 edges.
Answer: 12