Measurement and Geometry
Core ideas
Geometry questions combine formula recall with careful diagram reading. You must know perimeter and area of rectangles, triangles, parallelograms, trapezia and circles; volume and surface area of prisms and cylinders; angle facts for straight lines, triangles, parallel lines and polygons; Pythagoras' theorem; the trigonometric ratios; similarity and congruence; and unit conversion, including scale drawings and bearings.
Traps
- Confusing radius and diameter, especially in circle area and cylinder volume.
- Mixing units: converting one length to metres while leaving another in centimetres.
- Choosing the wrong side as the hypotenuse in Pythagoras' theorem - it is always opposite the right angle and always the longest side.
- Adding areas for a composite shape that actually needs an unshaded region subtracted.
- Calling two triangles congruent when only their angles match; equal angles give similarity, not congruence.
Worked example
Find the size of each interior angle of a regular pentagon. The angle sum of an n-sided polygon is (n - 2) × 180°. For n = 5: (5 - 2) × 180° = 540°. A regular pentagon has five equal angles, so each interior angle is 540° ÷ 5 = 108°.
Rule of thumb
Before calculating, write the formula, list the known values with their units, convert everything to a single unit, and only then substitute. Recording the formula first prevents the most common geometry errors.