GRADE 8 Mathematics GEOMETRY – Scale Drawing Notes

Mathematics — GEOMETRY

Subtopic: Scale Drawing (for age 13, Kenyan context)

A scale drawing is a picture or map drawn smaller or larger than the real thing. The scale tells us how drawing size relates to actual size. In Kenya we often use metres (m) and centimetres (cm). Remember: 1 m = 100 cm.

Important formulas

• Scale (ratio): drawing : actual (for example 1 : 100).
• To find drawing length: drawing = actual ÷ scale factor (when units are the same).
• To find actual length: actual = drawing × scale factor.
• If units differ, convert them to the same unit before using the formula (e.g., convert metres to centimetres).

How to use a scale (step-by-step)

1. Write the scale (example: 1 : 100).
2. Make sure actual measurement and drawing measurement use the same unit (both in cm or both in m).
3. Use the formula: drawing = actual ÷ scale (or actual = drawing × scale).
4. When drawing, measure carefully with a ruler and keep straight lines.

Worked example 1 (house plan)

A classroom measures 8 m by 6 m. Make a scale drawing using scale 1 : 100. (Meaning 1 cm on drawing = 100 cm = 1 m.)

Convert to cm: 8 m = 800 cm, 6 m = 600 cm. Using scale 1:100,

drawing length = actual ÷ 100

• Length = 800 ÷ 100 = 8 cm
• Width = 600 ÷ 100 = 6 cm

Worked example 2 (map distance)

Map scale is 1 : 50 000 (1 cm on map = 50 000 cm in real life). If two towns are 3.5 cm apart on the map, how far in kilometres?

actual = drawing × scale = 3.5 cm × 50 000 = 175 000 cm. Convert to metres: 175 000 ÷ 100 = 1 750 m = 1.75 km.

Quick tips

• If scale is 1 : 100, then 1 cm on drawing = 1 m in real life (because 100 cm = 1 m).
• Always check units: convert metres to centimetres before dividing by a scale like 100.
• For model cars or buildings, scales can be 1 : 18, 1 : 25, 1 : 100 etc. Smaller denominator → larger drawing/model.
• You can draw a scale bar: small segments labelled with real distances help users measure directly on the drawing.

Practice questions

1. Using scale 1 : 200, a school field is 90 m long. What is the length on the drawing in cm?
2. A toy model has scale 1 : 50. The real car is 4.2 m long. How long is the model in cm?
3. On a map with scale 1 : 100 000, two villages are 2.4 cm apart. What is the distance in km?
4. A plan uses scale 1 : 100. A cupboard drawn as 3 cm on the plan. What is the actual height in metres?

Answers (check your work)

1. 90 m = 9 000 cm. Drawing = 9 000 ÷ 200 = 45 cm.
2. 4.2 m = 420 cm. Model length = 420 ÷ 50 = 8.4 cm.
3. Actual = 2.4 × 100 000 cm = 240 000 cm = 2 400 m = 2.4 km.
4. Actual = 3 cm × 100 = 300 cm = 3.0 m.