66
Properties of area
Textbook: Part 2, lesson 66, pp. 84–86
GoalProperties of area: relations between area units and the area of a whole as the sum of its parts.
New words
area · yuzsquare decimetre · kvadrat detsimetrsquare metre · kvadrat metrpart · bo‘lak
Explanation
1 dm² = 100 cm², 1 m² = 100 dm² = 10 000 cm². Going from a bigger unit to a smaller one we multiply by 100, and the other way we divide by 100. The area of a rectangle is S = a × b. The area of a whole shape equals the sum of the areas of its parts, so the unpainted area = whole area − painted area.
Worked examples
4 dm² = 4 × 100 = 400 cm²; 500 dm² = 500 : 100 = 5 m².
From a 12 m × 8 m area a 5 m × 8 m part is painted: whole 96 m², painted 40 m², the rest 96 − 40 = 56 m².
Class activity
“Filling squares”: children divide a 10 cm × 10 cm square into 1 cm² cells and count to show that 1 dm² = 100 cm².
Practice
1
How many dm² is 3 m²?
300
2
How many m² is 700 dm²?
7
3
From a 20 cm × 15 cm rectangle a 20 cm × 6 cm part is painted. What is the unpainted area in cm²?
180
4
A field is 60 m × 40 m. The wheat on a 45 m × 40 m part has been harvested. What is the area of the unharvested part in m²?
600
5
How many cm² equal 5 dm²?
500