68
Finding area (practice)
Textbook: Part 2, lesson 68, pp. 90–92
GoalFinding the area of a polygon by splitting it into parts.
New words
part · bo‘lakright triangle · to‘g‘ri burchakli uchburchaksum · yig‘indidifference · ayirma
Explanation
To find the area of a complex shape we split it into rectangles and add their areas, or subtract the extra part from a big rectangle. An L-shape with parts 8 cm × 5 cm and 4 cm × 3 cm has area 8 × 5 + 4 × 3 = 52 cm². A right triangle is half of the matching rectangle: with legs 6 cm and 8 cm its area is 6 × 8 : 2 = 24 cm².
Worked examples
L-shape: 8 × 5 + 4 × 3 = 40 + 12 = 52 cm².
A 4 × 3 corner is cut from a 10 × 8 rectangle: 80 − 12 = 68.
Class activity
“Split and calculate”: draw L and T shapes in your notebook, split them into rectangles and find their areas.
Practice
1
An L-shaped room consists of two rectangles, 6 m × 4 m and 3 m × 2 m. What is its area in m²?
30
2
A 4 m × 3 m corner is cut from a 10 m × 8 m plot. What area in m² remains?
68
3
A right triangle has legs 6 cm and 8 cm. What is its area in cm²?
24
4
A cupboard front has 4 identical doors, each 35 cm × 50 cm. What is the total area of the doors in cm²?
7000