68
Area of irregular shapes
Textbook: Part 2, lesson 68, pp. 90–92
GoalFind the area of irregular shapes by splitting them or completing them.
New words
composite shape · murakkab shaklright triangle · to‘g‘ri burchakli uchburchaksubtracting · ayirishsplitting into parts · bo‘laklarga bo‘lish
Explanation
There are two ways to find the area of a composite shape: 1) split it into rectangles and add their areas; 2) complete it to a big rectangle and subtract the area of the added part. If we complete a right triangle with an identical triangle, we get a rectangle, so the triangle’s area is half the area of that rectangle.
Worked examples
An L-shape consists of a 10 m × 3 m rectangle and a 4 m × 5 m rectangle: 10 × 3 + 4 × 5 = 30 + 20 = 50 m².
A right triangle whose sides next to the right angle are 6 cm and 8 cm has area 6 × 8 : 2 = 24 cm².
Class activity
“Cut the shape”: children draw an L-shape on squared paper, find its area in two ways (splitting and completing) and compare the results.
Practice
1
A shape consists of a 12 cm × 4 cm and a 5 cm × 6 cm rectangle. What is its area in cm²?
78
2
A 15 m × 10 m plot contains a 4 m × 5 m pond. What is the area of the plot without the pond, in m²?
130
3
The sides next to the right angle of a right triangle are 10 dm and 6 dm. What is its area in dm²?
30
4
A 20 cm × 15 cm window opening is cut from a 60 cm × 40 cm board. What is the area of the remaining board in cm²?
2100