116
Polygons and prisms
Textbook: Part 4, lesson 116, pp. 25–27
GoalPolygons and prisms: bases and side faces; naming prisms; counting faces, edges and vertices.
New words
polygon · ko‘pburchakprism · prizmabase · asosside face · yon yoq
Explanation
A prism has two equal polygon faces opposite each other, and all its other faces are rectangles. The polygons are the bases and the rectangles are the side faces. The name depends on the base: triangular, pentagonal, hexagonal prism. A prism whose base has n sides has n + 2 faces, 3 × n edges and 2 × n vertices. A triangular prism has 5 faces, 9 edges and 6 vertices.
Worked examples
Pentagonal prism: 5 + 2 = 7 faces, 3 × 5 = 15 edges, 2 × 5 = 10 vertices.
Hexagonal prism: 8 faces, 18 edges, 12 vertices. A cuboid is a four-sided prism: 6, 12, 8.
Class activity
“Prism builders”: build models of a triangular and a four-sided prism from plasticine and sticks and count vertices and edges.
Practice
1
How many faces does a triangular prism have?
5
2
How many edges does a pentagonal prism have?
15
3
How many vertices does a hexagonal prism have?
12
4
A triangular prism has 3 side faces, each a 12 cm × 30 cm rectangle. What is their total area in cm²?
1080
5
How many faces does a prism with an eight-sided base have?
10