🎯 Learning Objectives
By the end of this lesson, you should be able to:
- Calculate actual lengths from scale drawings.
- Calculate actual areas using squared conversion factors.
- Keep linear and square units separate.
- Solve land-area and floor-plan problems.
🤔 Start with the Idea
Finding an area from a map requires more than converting one length. Since area is two-dimensional, the scale conversion must affect both dimensions.
📖 Area from a Map
If 1 cm represents 50 m, then:
1 cm² represents 50 m × 50 m = 2 500 m²
This is the area factor for the map.
Do not say 1 cm² represents 50 m². The conversion factor must be squared.
🎮 Explore the Scale
Change the map or drawing length and the scale value. Notice how the real distance changes proportionally.
🧠 Let’s Think Together
A rectangular plot is 6 cm by 4 cm on a plan with scale 1 cm represents 20 m.
Real dimensions: 6 × 20 = 120 m and 4 × 20 = 80 m.
Area = 120 × 80 = 9 600 m²
Answer: 9 600 m².
✏️ Practice Questions
Build confidence- A rectangle is 3 cm by 5 cm at 1 cm = 10 m. Find the real area.
- At RF 1 : 2 000, a square has map side 4 cm. Find its actual area in m².
- A field has map area 12 cm² at 1 cm = 25 m. Find its real area.
✅ Check your answers
- 1 500 m²
- 6 400 m²
- 7 500 m²
⚠️ Common Mistakes
- Using different units on the two sides of a ratio scale.
- Multiplying when the question requires division, or dividing when it requires multiplication.
- Leaving out the unit or using a linear unit for an area.
- Rounding too early in a multi-step calculation.
🎯 Exam Focus
Write what the scale means before calculating. Show unit conversions clearly, keep full calculator values until the final step, and include the correct unit in the answer.
📌 One-Minute Summary
- A scale connects a drawing or model to the corresponding real object.
- Use multiplication when moving from a drawing measurement to a real measurement.
- Use division when working backwards from real size to drawing size.
- Ratio scales require the same unit on both sides.
- Area changes by the square of the linear scale factor.