Length question
Use the linear scale directly.
🎯 Learning Objectives
By the end of this lesson, you should be able to:
- Choose between statement and RF methods.
- Work backwards to find a scale.
- Combine distance, scale factor and area factor.
- Explain and verify solutions.
🤔 Start with the Idea
This lesson brings together statement scales, representative fractions, scale drawings, linear scale factor and area factor. The challenge is deciding which relationship applies.
📖 Decide Before You Calculate
Area question
Square the linear scale factor or convert both dimensions.
Find the scale
Convert to the same units, then simplify the ratio.
🎮 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 plan shows a rectangular park as 7.2 cm by 4.5 cm. The real park is 360 m long.
Step 1: 360 m = 36 000 cm.
Step 2: Scale = 7.2 : 36 000 = 1 : 5 000.
Step 3: Real width = 4.5 × 5 000 = 22 500 cm = 225 m.
Step 4: Area = 360 × 225 = 81 000 m².
✏️ Practice Questions
Build confidence- A 15 km road is 6 cm on a map. Find the RF scale.
- Two similar plans have linear scale factor 3/2. Find the area factor.
- At RF 1 : 25 000, a rectangular map region is 8 cm by 5 cm. Find its real area in km².
- A model uses scale 1 : 40. A surface on the model has area 18 cm². Find the corresponding real area in m².
✅ Check your answers
- 1 : 250 000
- 9/4
- 2.5 km²
- 2.88 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.