GCSE Maths: Geometry & Measures — Revision Workbook

Inside GCSE Maths: Geometry & Measures — Revision Workbook

find missing angles on lines, at points and in triangles, quadrilaterals and parallel lines, work with interior and exterior angles of polygons, calculate area, perimeter, circumference and volume, then use Pythagoras’ theorem and SOHCAHTOA trigonometry on right-angled triangles, with bearings and similarity too. About 30 minutes.

Learning objectives

• angle rules — on a line, at a point, in triangles and quadrilaterals, and the parallel-line rules (alternate, corresponding and co-interior angles);
• interior and exterior angles of polygons, using (n − 2) × 180° and the 360° exterior-angle sum, plus the properties of common shapes;
• area, perimeter and circles — rectangle, triangle, parallelogram and trapezium areas, and circle area (πr²) and circumference (πd);
• volume and surface area of cuboids, prisms and cylinders;
• Pythagoras’ theorem (a² + b² = c²) and right-angled trigonometry (SOHCAHTOA), with bearings and similarity.

Activities in this book

1. Task 1 — Angles: Lines, Triangles & Parallel Rules

   angles on a straight line add to 180°, angles at a point add to 360°, the angles in a triangle add to 180° and the angles in a quadrilateral add to 360°. Between parallel lines, alternate angles are equal, corresponding angles are equal, and co-interior (allied) angles add to 180°.

2. Task 2 — Polygons & Shape Properties

   the interior angles of a polygon with n sides add up to (n − 2) × 180°. The exterior angles of any polygon always add up to 360°, so a regular polygon’s exterior angle is 360° ÷ n, and its interior angle is 180° − the exterior angle.

3. Task 3 — Area, Perimeter & Circles

   area of a rectangle = base × height; triangle = ½ × base × height; parallelogram = base × height; trapezium = ½(a + b) × height. For a circle, area = πr² and circumference = πd. Each circle question tells you whether to use π = 3.14 or to leave the answer in terms of π.

4. Task 4 — Volume, Pythagoras & Trigonometry

   volume of a prism = area of cross-section × length; volume of a cylinder = πr²h. Pythagoras’ theorem says a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle). For angles, use SOHCAHTOA: sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.

5. Task 5 — Geometry at Home

   geometry is everywhere at home — the corner of a table, a tin of beans, a tiled floor. Measuring and estimating real shapes is exactly the reasoning GCSE examiners want to see.

Suggestions for teaching

• Name the rule. Before finding an angle, ask learners to state which rule they are using — the marks in the exam come from the reasoning.
• The polygon formulas. Model (n − 2) × 180° for the interior-angle sum and 360° ÷ n for a regular exterior angle.
• Read the π instruction. Be explicit about when to use π = 3.14 and when to leave an answer in terms of π — both appear in GCSE papers.
• Pythagorean triples. Teach 3-4-5 and 5-12-13 so learners can spot exact answers, then check with a² + b² = c².
• SOHCAHTOA. Practise labelling opposite, adjacent and hypotenuse first, then choosing sin, cos or tan before reaching for a calculator.