Geometry and Measures
This domain covers angle facts, polygons, circles, mensuration, transformations, similarity and bearings. Questions usually supply a diagram; the marks are for identifying the correct property and applying it with consistent units.
Rules
- Angles on a straight line sum to 180°, around a point 360°, in a triangle 180°. The exterior angle of a triangle equals the sum of the two opposite interior angles.
- Interior angle sum of an n-sided polygon: (n−2)×180°. For a regular polygon, each exterior angle is 360°/n.
- Circle: circumference = 2πr, area = πr². Arc length = (θ/360)×2πr; sector area = (θ/360)×πr².
- Volume of a prism = area of cross-section × length; for a cylinder V = πr²h.
- Similar shapes: corresponding lengths scale by k, areas by k², volumes by k³.
Worked example
A sector has radius 9 cm and angle 140°. Arc length = (140/360)×2π×9 = (7/18)×18π = 7π ≈ 22.0 cm. Sector area = (140/360)×π×9² = (7/18)×81π = 31.5π ≈ 99.0 cm². Use the radius, not the diameter, and keep π in the working until the final value.
Traps
Using the diameter in place of the radius; adding a sector angle to 180° instead of using the full circle; mixing cm and m; giving a bearing as 45° rather than 045°; assuming a diagram is drawn to scale. For similar solids, remember to cube the length scale factor.