51
Solid figures. Polyhedra
Textbook: Part 2, lesson 51, pp. 56–59
GoalTell flat from solid shapes; polyhedron, prism, pyramid, vertices, edges and faces.
New words
polyhedron · ko‘pyoqprism · prizmapyramid · piramidaface, edge, vertex · yoq, qirra, uch
Explanation
Flat shapes lie in one plane, while solid shapes (bodies) are three-dimensional. A body whose boundary consists of flat polygons is a polyhedron. The polygons are its faces, their sides are its edges and their corners are its vertices. A prism has two faces (bases) that are equal polygons, and its other faces (lateral faces) are quadrilaterals. A pyramid has one polygon face (the base), and its lateral faces are triangles sharing one common vertex. A cylinder, a cone and a ball are not polyhedra, because their boundary has no flat polygons; the surface of a ball is called a sphere.
Worked examples
A triangular prism has 5 faces (2 triangular bases and 3 quadrilateral lateral faces), 9 edges and 6 vertices.
A quadrilateral pyramid has 5 faces (1 base and 4 triangles), 8 edges and 5 vertices. A cylinder, however, is not a polyhedron.
Class activity
“Objects at home”: find 6 objects at home (box, ball, bottle, jar, juice carton, etc.) and sort them into «polyhedron» and «not a polyhedron».
Practice
1
How many faces does a pentagonal prism have?
7
2
How many edges does a triangular pyramid have?
6
3
Which of these is a polyhedron: cone, cube, ball?
cube
4
Why is a cylinder not a polyhedron?
Its lateral surface is curved, not a flat polygon.