Stage 11 · Shape & space
Solids
Count the base's sides, then work it out.
How to do it
Method
Count the base's sides, then work it out
Hexagonal prism's edges: 6 × 3 = 18
Another way
Count them
6 + 6 + 6 = 18
In full
A prism has two matching bases, top and bottom, and rectangles round the side; a pyramid has one base and triangles round the side, meeting at a point at the top. A base with 6 sides makes a hexagonal prism or pyramid; a cube and a cuboid are four-sided prisms. When you count faces, edges and vertices, count the hidden ones (the dashed lines) too. Quicker: count the base's sides, then work it out. A prism: faces = sides + 2, edges = sides × 3, vertices = sides × 2; a pyramid: faces = sides + 1, edges = sides × 2, vertices = sides + 1. A hexagonal prism's edges: 6 × 3 = 18; a pentagonal pyramid's faces: 5 + 1 = 6; a cuboid's vertices: 4 × 2 = 8. Another way: count them one by one; a hexagonal prism has 6 edges on top, 6 at the bottom and 6 up the side, 6 + 6 + 6 = 18 — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A hexagonal prism has ? faces
Show the answer and working
Answer: A hexagonal prism has 8 faces
A prism has 2 bases and 6 faces round the side: 6 + 2 = 8, so 8 faces
Example 2
A cuboid has ? vertices
Show the answer and working
Answer: A cuboid has 8 vertices
The top and the bottom have 4 vertices each: 4 × 2 = 8, so 8 vertices
Example 3
A triangular pyramid has ? edges
Show the answer and working
Answer: A triangular pyramid has 6 edges
The base has 3 edges, and one runs from the top to each corner of it: 3 × 2 = 6, so 6 edges
Example 4
This prism has ? edges
Show the answer and working
Answer: This prism has 30 edges
Its base is a decagon, with 10 sides. The top and the bottom have 10 edges each, and 10 more run up the side: 10 × 3 = 30, so 30 edges
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