119
Polygons and pyramids
Textbook: Part 4, lesson 119, pp. 34–36
GoalPolygons and pyramids: counting faces, edges and vertices of a pyramid with an n-sided base.
New words
polygonal pyramid · ko‘pburchakli piramidanumber of edges · qirralar soninumber of vertices · uchlar soninumber of faces · yoqlar soni
Explanation
A pyramid whose base has n sides has n + 1 faces (1 base and n triangles), 2 × n edges (n on the base and n side edges) and n + 1 vertices (n on the base and the apex). A pentagonal pyramid has 6 faces, 10 edges, 6 vertices; a hexagonal pyramid has 7 faces, 12 edges, 7 vertices. Compare with a prism: a prism has two bases, a pyramid one.
Worked examples
Pentagonal pyramid: 5 + 1 = 6 faces; 2 × 5 = 10 edges; 5 + 1 = 6 vertices.
If a pyramid has 7 faces, its base has 6 sides: a hexagonal pyramid.
Class activity
“Which solid?”: the teacher says the numbers of faces, edges and vertices (6, 10, 6) and children find whether it is a pyramid or prism and its name.
Practice
1
How many faces does a pentagonal pyramid have?
6
2
How many edges does a hexagonal pyramid have?
12
3
How many vertices does a pyramid with an eight-sided base have?
9
4
A pyramid has 7 faces. How many sides does its base have?
6
5
A model of a square pyramid needs one stick per edge. How many sticks are needed for 10 such models?
80