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Geometry and Measures (National 4)

Measurement, Scale and Navigation

Measurement questions use units, scale drawings, bearings, first-fit packing, tolerance and related quantities in practical planning situations.

Qualification focus: Related quantities · Scale drawings · Navigation course · First-fit packing · Tolerance and accuracy

Topic explanation

Always check the unit before calculating. A correct number with the wrong unit can still be wrong.

Scale drawings use a fixed relationship between drawing length and real length. Apply the same scale every time.

Bearings start at north, turn clockwise and use three digits, such as 045°. A navigation route also needs its distance or map scale.

First-fit packing depends on arrival order. Tolerance decisions include values exactly on the stated minimum or maximum unless the question says otherwise.

Quick methods

Convert units
Make every measurement use a compatible unit before calculating.
Scale drawing
Use the given scale consistently to move between drawing and real dimensions.
Bearing
Measure clockwise from north and write a three-figure bearing.
First fit
Keep the item order and try each existing container from the first one.
Tolerance
Target minus tolerance to target plus tolerance gives the inclusive acceptable range.
Related quantity
Calculate the measurement first, then round up only when whole packs or items are required.

Worked examples

Example 1

Change 3.5 m into centimetres.

  1. There are 100 cm in 1 m.
  2. Centimetres are smaller than metres, so multiply by 100.
  3. 3.5 × 100 = 350

So: 3.5 m = 350 cm

Example 2

A rectangle is 8 cm long and 5 cm wide. What is its perimeter?

  1. Perimeter means the distance around the outside.
  2. Add all four sides: 8 + 5 + 8 + 5.
  3. 8 + 5 + 8 + 5 = 26

So: The perimeter is 26 cm.

Example 3

On a scale drawing, 1 cm represents 4 m. A wall is 6.5 cm on the drawing. What is the real length?

  1. Each 1 cm on the drawing stands for 4 m in real life.
  2. Multiply the drawing length by 4.
  3. 6.5 × 4 = 26

So: The real wall length is 26 m.

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