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MathidiaMathematics Academy
Circles and constructions
Lesson 55 of 75
Review

Scale drawings and constructions

Objective. Construct and interpret accurate scale diagrams.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Scale drawings and constructions represent real objects at a reduced or enlarged size using a consistent ratio, such as 1 cm representing 5 m, alongside accurate geometric constructions using a ruler and compasses. To interpret a scale drawing, measure a length on the drawing and multiply by the scale factor to find the real-world distance, or divide a real distance by the scale factor to find the drawn length. For constructions, a perpendicular bisector is drawn by opening compasses to more than half the line's length and drawing arcs from each end that intersect above and below the line. Precision with compasses and a sharp pencil is essential for accurate constructions that will be checked against required tolerances.

Worked example

A scale drawing uses a scale of 1 cm to 4 m. A wall measures 7 cm on the drawing. Find the real length of the wall.

1 … 4
Illustrated card showing 1 … 4
  1. 1Identify the scale: 1 cm on the drawing represents 4 m in real life.
  2. 2The wall's drawn length is 7 cm.
  3. 3Multiply the drawn length by the scale factor: 7 × 4.
  4. 47 × 4 = 28.

Answer: 28 m

Concept mastery

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Practice

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Common mistake. Pupils often compute real-world distances by dividing instead of multiplying by the scale factor, confusing which direction the conversion should go. Multiply the drawn length by the scale factor to find the real distance, not divide.

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