Geometry and Measurement
Geometry and Measurement tests perimeter, area, volume, surface area, angle facts, Pythagoras' theorem and scale drawings in practical settings. Typical tasks include costing carpet, paint or fencing, reading floor plans, and converting between metric units.
Core rules
- Perimeter is the distance around a shape; area is measured in square units; volume in cubic units.
- Rectangle: area = length × width; triangle: area = ½ × base × height; circle: area = πr², circumference = 2πr.
- Volume of a rectangular box = length × width × height.
- Pythagoras: in a right triangle, a² + b² = c², where c is the hypotenuse.
- Convert units before calculating: 1 m = 100 cm, 1 m² = 10,000 cm², 1 m³ = 1,000,000 cm³.
- A scale of 1:50 means 1 cm on the plan represents 50 cm in reality.
Worked example
A room is 4.2 m long, 3.5 m wide and 2.4 m high. Find the floor area and the volume. Floor area = 4.2 × 3.5 = 14.7 m². Volume = 4.2 × 3.5 × 2.4 = 35.28 m³. If carpet costs €18 per m², carpet cost = 14.7 × 18 = €264.60.
Traps that cost marks
- Using diameter instead of radius in circle formulas.
- Adding lengths in different units, e.g. 4 m + 35 cm.
- Confusing area and perimeter when buying skirting or carpet.
- Forgetting that paint may need two coats, or that doors/windows are not painted.