117
A prism and its net
Textbook: Part 4, lesson 117, pp. 28–30
GoalThe net of a prism: bases and side faces; lateral and total surface area.
New words
net · yoyilmalateral (side) surface · yon sirttotal surface · to‘la sirtperimeter of the base · asos perimetri
Explanation
The net of a prism has two bases and the side faces. The side faces form a strip of joined rectangles. The net of a triangular prism: 2 triangles and 3 rectangles; of a pentagonal prism: 2 pentagons and 5 rectangles. Lateral surface area = perimeter of the base × height of the prism. Total surface area = 2 base areas + lateral surface area.
Worked examples
A prism with a 4 cm square base and height 10 cm: bases 2 × 16 = 32 cm², lateral surface 16 × 10 = 160 cm², total 192 cm².
Each side face of a triangular prism is 5 cm × 12 cm: lateral surface 3 × 60 = 180 cm².
Class activity
“Build the net”: children draw the net of a triangular prism on squared paper, cut it out (with an adult's help), fold and glue it.
Practice
1
How many pieces (bases and side faces) are in the net of a triangular prism?
5
2
How many rectangles are in the net of a pentagonal prism?
5
3
A triangular prism has two bases of 6 cm² each and three side faces of 20 cm² each. What is its total surface area in cm²?
72
4
Each side face of a prism with a square base is an 8 cm × 15 cm rectangle. What is the lateral surface area in cm²?
480
5
A prism has a square base of side 4 cm and height 10 cm. What is its total surface area in cm²?
192