All skills Math

Learn Index · Ratios, Rates, and Proportions Grade 6–8

Scale drawings and maps

A drawing or map where lengths are in a fixed ratio to real lengths.

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Drawing big things small

A scale drawing shows an object accurately but at a different size. Maps, floor plans, blueprints and model kits are all scale drawings. The scale tells how drawing lengths relate to real lengths.

Ways to write a scale

Form Example Meaning
Words 1 cm represents 5 km each cm on the map = 5 km real
With units 1 cm : 5 km same
Ratio scale 1:500,000 1 unit on the map = 500,000 of the same unit in reality
Bar scale a line marked 0–10 km measure with a ruler and compare

Converting between a ratio and a unit scale

1:500,000 means 1 cm = 500,000 cm = 5,000 m = 5 km.

From drawing to real

Multiply by the scale.

Example: A map scale of 1 cm : 20 km. Two cities are 7.5 cm apart.

Actual distance = 7.5 × 20 = 150 km.

From real to drawing

Divide by the scale.

Example: A floor plan uses 1 cm : 0.5 m. A room is 4 m long.

Drawing length = 4 ÷ 0.5 = 8 cm.

Using proportions

Any scale problem can be solved as a proportion:

drawing/real = drawing/real

Example: Scale 2 cm : 3 m. A wall is 10.5 m. How long on the drawing?

2/3 = x/10.5 → 3x = 21 → x = 7 cm.

Making a scale drawing

  1. Measure the real object.
  2. Choose a scale that fits your paper.
  3. Divide every real length by the scale.
  4. Draw accurately with a ruler; keep the angles the same.
  5. Write the scale on the drawing.

Area on scale drawings

Areas don’t scale the same way as lengths. If 1 cm = 2 m, then 1 cm² = 4 m².

Worked examples

Example 1: Scale 1:100. A drawing of a door is 2.1 cm tall. Real height?

2.1 × 100 = 210 cm = 2.1 m.

Example 2: A model car is built at 1:24. The real car is 4.8 m long. Model length?

480 cm ÷ 24 = 20 cm.

Example 3: On a 1 cm : 50 km map, a lake is 3.4 cm wide. Real width?

170 km.

Common mistakes

  • Mixing units: forgetting that 1:100,000 uses the same unit on both sides.
  • Multiplying when you should divide (real to drawing).
  • Scaling area like length.

Try it yourself

  1. Scale 1 cm : 4 km. Map distance 6.5 cm. Real distance?
  2. Scale 1:50. A table is 1.5 m long. Drawing length?
  3. Write 1 cm : 2 km as a ratio scale.
  4. A 3 cm × 2 cm room on a 1 cm : 3 m plan. Real area?

Answers: 1) 26 km 2) 3 cm 3) 1:200,000 4) 9 m × 6 m = 54 m²

Quick recap

  • A scale drawing keeps shape but changes size.
  • Drawing → real: multiply; real → drawing: divide.
  • Use matching units for a ratio scale.