38
Units of area
Textbook: Part 2, lesson 38, pp. 9–12
GoalKnow the units of area (mm², cm², dm², m², ar, ha, km²) and the relations between them; convert units.
New words
square metre · kvadrat metrare (sotix) · ar (sotix)hectare · gektarsquare kilometre · kvadrat kilometr
Explanation
Area is measured in square units. Lengths satisfy 1 cm = 10 mm, 1 dm = 10 cm, 1 m = 10 dm, 1 km = 1 000 m, but each step of area units is 100 times: 1 cm² = 100 mm², 1 dm² = 100 cm², 1 m² = 100 dm² = 10 000 cm². Large plots are measured in ares (sotix) and hectares: 1 ar = 10 m × 10 m = 100 m², 1 ha = 100 m × 100 m = 10 000 m² = 100 ar, 1 km² = 100 ha = 1 000 000 m². If the sides are given in different units, first convert them to one (usually the smaller) unit, then find the area.
Worked examples
Length 2 m 50 cm, width 40 cm: 250 cm × 40 cm = 10 000 cm² = 1 m².
A plot 30 m × 20 m = 600 m² = 6 ar. A field 400 m × 250 m = 100 000 m² = 10 ha.
Class activity
“Unit staircase”: draw a staircase 1 km² → 1 ha → 1 ar → 1 m² → 1 dm² → 1 cm² → 1 mm² on the board; at each step write “× 100” or “: 100” and pupils convert units.
Practice
1
How many cm² is 3 dm²?
300
2
A field measures 400 m × 250 m. What is its area in hectares?
10
3
How many m² is 8 ar?
800
4
Why is 1 m² equal to 10 000 cm² and not 100 cm²?
1 m = 100 cm, so 1 m² = 100 cm × 100 cm = 10 000 cm².