Prism & pyramid
FoundationPrism: 2 congruent bases; pyramid: 1 base + apex.
- A prism: two identical parallel bases, rectangular sides
- A pyramid: one base, triangular faces meeting at an apex
- Named by the base: triangular prism, square pyramid
1Summary 重點摘要
Prism: 2 congruent bases; pyramid: 1 base + apex.
2Vocabulary cards Vocabulary
A solid with two identical parallel bases and rectangular side faces.
One base with triangular faces meeting at an apex.
The face that names it: triangle base → triangular prism; square base → square pyramid.
The point where all a pyramid's triangular faces meet.
A prism with two triangle bases, like a chocolate bar.
A prism with rectangle bases, e.g. a shoebox.
A square base with four triangular faces, like the pyramids of Egypt.
Flat faces, edges and corners; a cuboid has 6 faces, 12 edges, 8 vertices.
3Step by step Steps
- Part 1: Features of a prismLook at a triangular chocolate bar: the front and back faces are identical parallel triangles, and all the side faces around it are rectangles. Any solid with two identical, parallel bases and rectangular side faces is a prism.
- Part 2: Features of a pyramidPicture an Egyptian pyramid: a square base, four triangular faces, all rising toward the middle from above and meeting at one point called the apex. A solid with only one base, whose side faces all meet at a single apex, is a pyramid.
- Part 3: Named by the baseThe names of prisms and pyramids come from the shape of the base. A prism with triangular bases is a triangular prism; with rectangular bases it is a cuboid, the most familiar four-sided prism. A pyramid with a square base is a square pyramid, like the pyramids in Egypt.
- Part 4: Counting faces, edges and verticesA cuboid has 6 faces, 12 edges and 8 vertices; a square pyramid has 5 faces (1 square base plus 4 triangles), 8 edges and 5 vertices. Counting once on a real block or box is more reliable than memorising numbers.
- Part 5: Telling prisms and pyramids apartThere are two quick checks. First, count the bases: a prism has 2 identical bases, a pyramid has only 1. Second, look for an apex: a pyramid has one, a prism has none. A shoebox is a prism; an Egyptian pyramid is a pyramid.
- Part 6: Solids around usPrisms: shoeboxes, cans (cylinders), triangular chocolate bars, the columns of a house. Pyramids: Egyptian pyramids, party hats (cones), the upper part of a funnel. When you meet a solid, count the bases and look for the apex, and you can name it.
4Diagrams Diagrams
5Worked example Example
Example: a solid has 1 square base and 4 triangular side faces, and all the triangles meet at one point. (1) Is it a prism or a pyramid? (2) How many faces and vertices does it have?
- (1) Count the bases: only 1, with the other faces meeting at a point, so it is a pyramid.
- Look at the base shape: it is a square, so it is a square pyramid, the pyramid shape.
- (2) Count faces: 1 square base plus 4 triangular sides makes 5 faces in all.
- Count vertices: the 4 corners of the base plus 1 apex makes 5 vertices in all.
- Answer: Answer: (1) it is a pyramid, precisely a square pyramid; (2) it has 5 faces and 5 vertices. The keys are the number of bases and the apex: a solid with one base whose faces meet at a point is a pyramid.
6Common mistakes Mistakes
7Quick check Quick check
Q1What solid is a shoebox?
Q2What solid is an Egyptian pyramid?
Q3How many bases does a prism have?
Q4A triangular chocolate bar is what prism?
Q5How many faces does a square pyramid have?
8Recap Recap
- A prism: two identical parallel bases, rectangular sides
- A pyramid: one base, triangular faces meeting at an apex
- Named by the base: triangular prism, square pyramid
- Count bases and hunt the apex for a quick check
- Shoeboxes are prisms; pyramids are pyramids