3-D figures · Ages 12–13
Prisms, pyramids and round solids
Prism: n + 2 faces, 3n edges, 2n vertices; pyramid: n + 1, 2n, n + 1.
How to do it
Method
Prism: n + 2 faces, 3n edges, 2n vertices; pyramid: n + 1, 2n, n + 1
A hexagonal prism's edges: 6 top + 6 bottom + 6 upright = 18
Another way
Count from the faces
Hexagonal prism: (6 × 4 + 2 × 6) ÷ 2 = 18
In full
A right prism has two equal, parallel bases joined by rectangles; on an n-sided base it is an n-sided prism. A pyramid has one base, and its triangular sides meet at the apex; on an n-sided base it is an n-sided pyramid. A cylinder has two circular bases and one curved surface, a cone a circular base, a curved surface and an apex, and a sphere one curved surface only. Count faces, edges and vertices layer by layer: an n-sided prism has n edges round the top, n round the bottom and n upright, 3n in all; n vertices top and bottom, 2n; and n sides plus 2 bases, n + 2 faces. An n-sided pyramid has n base edges and n slanting ones, 2n; n + 1 vertices; n + 1 faces. Or count from the faces: add up every face's sides, and each edge has been counted twice, so the edges are half the total. A solid whose faces are all equal regular polygons, the same number meeting at every vertex, is a regular polyhedron.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The picture shows a right prism on a regular polygon. What is it called?
- A. A prism on a 5-sided base
- B. A pyramid on a 5-sided base
- C. A prism on a 6-sided base
- D. A prism on a 7-sided base
Choose the right answer
Show the answer and working
Answer: A. A prism on a 5-sided base
Two parallel bases, rectangular sides, and 5 sides to the base: a prism on a 5-sided base.
Example 2
A pyramid on a 4-sided base has faces, edges and vertices.
Fill in each blank
Show the answer and working
Answer: 5, 8, 5
Faces: the base and 4 triangles, 5; edges: 4 round the base and 4 slanting, 8; vertices: 4 round the base and 1 at the top, 5.
Example 3
A prism has 30 edges. How many sides does its base have?
Show the answer and working
Answer: 10 sides
A prism has 3 times as many edges as its base has sides (top, bottom and upright): 30 ÷ 3 = 10.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A prism on a 7-sided base has faces, edges and vertices.
Fill in each blank
Answer:
2.A prism has 21 edges. How many sides does its base have?
Answer:
3.A pyramid on a 10-sided base has faces, edges and vertices.
Fill in each blank
Answer:
4.Which solid has 7 faces, 15 edges and 10 vertices?
- A
- B
- C
- D
Choose the right picture
Answer:
5.A pyramid's edges and vertices number 13 in all. How many faces does it have?
Answer:
All the answers
- 1. 9, 21, 14
- 2. 7 sides
- 3. 11, 20, 11
- 4. C
- 5. 5 faces
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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