Geometry
Geometry
This domain tests angle facts, triangle properties, Pythagoras’ theorem, perimeter, area, and simple volume. Questions are usually multi-step: find a missing angle, then use it to calculate a length or area. Draw a quick sketch and label known values before choosing a formula.
Core rules
- Angles on a straight line add to 180°; angles around a point add to 360°; vertically opposite angles are equal.
- The interior angles of a triangle sum to 180°; a quadrilateral sums to 360°. In an isosceles triangle, base angles are equal.
- Pythagoras: in a right triangle, a² + b² = c², where c is the hypotenuse. Use it to find a missing side, not just the hypotenuse.
- Area formulas: rectangle lw; triangle ½bh; circle πr². Circumference is 2πr or πd. Volume of a cuboid is lwh.
- Similar shapes have equal corresponding angles and proportional sides; scale factors apply to lengths, and squared scale factors to areas.
Worked example
A right triangle has legs 6 cm and 8 cm. Find the hypotenuse and area. Hypotenuse: c² = 6² + 8² = 36 + 64 = 100, so c = 10 cm. Area: ½ × 6 × 8 = 24 cm². The perimeter is 6 + 8 + 10 = 24 cm.
Traps
Using the diameter as the radius in circle formulas; confusing area and perimeter; forgetting to square both legs before adding; using Pythagoras on a non-right triangle; and giving units squared for a length.