Worked Example

Question: A map has a scale of 1:40,000. If two buildings are 4 cm apart on the map, what is the real distance?

• Solution:

• $4 \times 40,000 = 160,000 cm$

• Convert to km: $160,000 \div 100,000 = 1.6$ $km$

• Answer: $1.6 km$

Worked Example

Question: A bar scale shows 1 segment = 10 m. If the measured length on the map is 3 segments, what is the real-world distance?

• Solution:
• $3 \times 10 = 30 m$
• Answer: $30 m$

Worked Example:

A bedroom measures 3.5 m by 4 m. Convert these dimensions to a scale of 1:50 for a floor plan.

4. Width:

• Real measurement: 3.5 m
• Conversion: $\text{m} \times 100 = 350 \, \text{cm}$
• Scaled: $350 \div 50 = 7 \, \text{cm}$

5. Length:

• Real measurement: 4 m
• Conversion: $4 \, \text{m} \times 100 = 400 \, \text{cm}$
• Scaled: $400 \div 50 = 8 \, \text{cm}$

6. Other objects:

• Bedside table scaled to $1.62cm$ by $0.8cm$.

Activity 3: Drawing a Scaled Plan

• Scenario: Your school is building a new classroom. Dimensions:
• Walls: $5m$ each
• Door: $810mm$
• Windows: $1,000mm$ Tasks:

7. Draw a scaled plan (1:50).

• Convert real-life measurements to scaled dimensions.

8. Window Blind Calculation:

• Total length = $5 \times 1 \, \text{m} = 5,000 \, \text{mm}$

9. Material Cost:

• Fabric: $R60$ per metre. Total cost = $R60 \times 5 = R300$

10. Tiles Needed:

• Tile area = $25m^2$. Number of boxes required: 7.

11. Cost of Tiles:

• Cost per box = $R150$. Total = $R1,050$.