Conversion of Area Units
When working with area, you need to convert between different units — square centimetres (cm²), square metres (m²), hectares, and square kilometres (km²).
The key difference from length conversion: area conversions involve squaring the length factor. If 1 m = 100 cm, then 1 m² = 100 × 100 = 10,000 cm².
What is Conversion of Area Units - Grade 7 Maths (Perimeter and Area)?
Area Unit Conversions:
- 1 cm² = 100 mm²
- 1 m² = 10,000 cm²
- 1 km² = 1,000,000 m²
- 1 hectare = 10,000 m²
- 1 km² = 100 hectares
- 1 m² = 10,000 cm² = 1,000,000 mm²
Conversion of Area Units Formula
1 m² = 10,000 cm²
1 hectare = 10,000 m²
1 km² = 100 hectares
Key rule: When converting area units, square the linear conversion factor.
Types and Properties
Common Conversions:
- cm² to m²: Divide by 10,000.
- m² to cm²: Multiply by 10,000.
- m² to hectares: Divide by 10,000.
- hectares to m²: Multiply by 10,000.
- km² to hectares: Multiply by 100.
Solved Examples
Example 1: cm² to m²
Problem: Convert 50,000 cm² to m².
Solution:
- 1 m² = 10,000 cm²
- 50,000 cm² = 50,000 ÷ 10,000 = 5 m²
Answer: 5 m².
Example 2: m² to hectares
Problem: A field has area 75,000 m². Express in hectares.
Solution:
- 1 hectare = 10,000 m²
- 75,000 ÷ 10,000 = 7.5 hectares
Answer: 7.5 hectares.
Example 3: km² to m²
Problem: Convert 2.5 km² to m².
Solution:
- 1 km² = 1,000,000 m²
- 2.5 × 1,000,000 = 2,500,000 m²
Answer: 2,500,000 m².
Example 4: Word Problem
Problem: A rectangular plot is 200 m × 150 m. Express its area in hectares.
Solution:
- Area = 200 × 150 = 30,000 m²
- 30,000 ÷ 10,000 = 3 hectares
Answer: 3 hectares.
Real-World Applications
Real-world uses:
- Agriculture: Farm areas measured in hectares.
- Real estate: Plot sizes in m² or sq ft.
- Geography: Country/city areas in km².
Key Points to Remember
- Square the linear conversion factor for area conversions.
- 1 m² = 10,000 cm² (not 100).
- 1 hectare = 10,000 m².
- 1 km² = 100 hectares = 1,000,000 m².
Practice Problems
- Convert 3 m² to cm².
- Convert 45,000 m² to hectares.
- Convert 0.5 km² to m² and hectares.
- A garden is 50 m × 20 m. Express area in cm² and hectares.
Frequently Asked Questions
Q1. Why do we square the conversion factor for area?
Area is length × length. If 1 m = 100 cm, then 1 m² = 1 m × 1 m = 100 cm × 100 cm = 10,000 cm². Both dimensions are converted.
Q2. What is a hectare?
A unit of area equal to 10,000 m², commonly used for measuring land area.
Q3. How many cm² in 1 m²?
10,000 cm² (100 × 100, not just 100).
