Bearings and MensurationEdexcel GCSE Maths: Revision notes

Section 1

Three-Figure Bearings

A bearing gives a direction as an angle measured clockwise from North, always written using three figures (e.g. 007°, 090°, 245°).

Key facts:

Bearings are always between 000° and 360°
The bearing from A to B and the bearing from B to A differ by exactly 180° (a 'back bearing')
Bearing problems are solved using angle facts on parallel lines (alternate and co-interior angles, since North lines at different points are parallel) and angle facts in triangles

Key termsbearingback bearing

Example

If the bearing of B from A is 065°, the bearing of A from B is 065° + 180° = 245°.

Section 2

Maps and Scale Drawings

A scale drawing represents real-life lengths in proportion, using a stated scale (e.g. 1 cm represents 5 m, or a ratio such as 1 : 500).

Real-life length = measured length × scale factor
Measured length = real-life length ÷ scale factor

Bearing problems are frequently combined with scale drawings and maps, so both skills are often needed together in the same question.

Key termsscale

Section 3

Perimeter and Area of Standard Shapes

Perimeter is the total distance around the outside of a shape (add up all the sides). Area is the amount of surface a shape covers.

Shape	Area formula
Triangle	½ × base × height
Rectangle	length × width
Parallelogram	base × height
Trapezium	½ × (sum of parallel sides) × height

Always use the perpendicular (vertical) height in these formulae, not a slanted side.

Key termsperimeterarea

Common mistake

For a parallelogram or triangle, using a slanted side instead of the perpendicular height gives the wrong area.

Section 4

Composite Shapes

A composite shape is made by combining two or more standard shapes. To find its area:

Split the composite shape into simple shapes (triangles, rectangles, etc.)
Calculate the area of each part separately
Add the areas together (or subtract, if one shape has been cut out of another)

Finding any missing lengths first (using given dimensions and the properties of the shapes involved) is often the key step.

Key termscomposite shape

Section 5

Circumference and Area of Circles

For a circle of radius r and diameter d:

Circumference = 2πr = πd
Area = πr²

These formulae also apply to semicircles and quarter-circles by taking the appropriate fraction of the full circle's circumference or area, and are essential for solving area/perimeter problems involving unknown lengths.

Key termscircumference

Example

A circle has radius 5 cm. Circumference = 2π × 5 = 10π ≈ 31.4 cm; Area = π × 5² = 25π ≈ 78.5 cm².

Must Know

Bearings are three-figure angles measured clockwise from North; back bearings differ by 180°
Bearing problems use parallel line angle facts (North lines are parallel) and triangle angle facts
Scale drawings: real-life length = measured length × scale factor
Area formulae: triangle = ½bh, rectangle = lw, parallelogram = bh, trapezium = ½(a+b)h — always use perpendicular height
Composite shape area = sum (or difference) of the areas of its simple parts
Circle circumference = 2πr = πd; circle area = πr²

That's the notes covered.

Carry on to the next subtopic.