120
A pyramid and its net
Textbook: Part 4, lesson 120, pp. 37–39
GoalThe net of a pyramid: the base and side faces; total surface area.
New words
net of a pyramid · piramida yoyilmasitriangular face · uchburchak yoqbase · asostotal surface · to‘la sirt
Explanation
The net of a pyramid has one base and the side faces, which are triangles attached to the sides of the base. The net of a square pyramid: 1 square and 4 triangles; of a triangular pyramid: 4 triangles; of a pentagonal pyramid: 1 pentagon and 5 triangles. Total surface area = area of the base + sum of the areas of all side faces.
Worked examples
A pyramid with a base of 36 cm² and 4 side faces of 30 cm² each: 36 + 4 × 30 = 156 cm².
A triangular pyramid with all 4 faces 9 cm² each: 4 × 9 = 36 cm².
Class activity
“Pyramid net”: children draw the net of a square pyramid on squared paper, cut it out (with an adult's help) and fold it into a pyramid.
Practice
1
How many pieces are in the net of a square pyramid?
5
2
How many triangles are in the net of a triangular pyramid?
4
3
A pyramid has a base of 36 cm² and 4 side faces of 30 cm² each. What is its total surface area in cm²?
156
4
How many triangles are in the net of a pentagonal pyramid?
5
5
Each of the 4 faces of a triangular pyramid is 9 cm². What is its total surface area in cm²?
36