Geometry and Measures: shape, space and trigonometry
What Geometry and Measures tests
Geometry and Measures covers angle facts, triangles and polygons, circles, perimeter, area and volume, Pythagoras' theorem, right-angled trigonometry, coordinate geometry and transformations. Foundation questions often supply a diagram; you must select the correct formula and give units.
Core rules
- Angles on a straight line add to 180°; angles at a point add to 360°; vertically opposite angles are equal.
- The angles of a triangle add to 180°. In an isosceles triangle, base angles are equal.
- Pythagoras: in a right-angled triangle, a² + b² = c², where c is the hypotenuse.
- Trigonometry: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
- Area of a circle = πr²; circumference = 2πr. Volume of a prism = cross-sectional area × length.
Worked example
A right-angled triangle has hypotenuse 13 cm and one shorter side 5 cm. Find the other shorter side and the area. Let the unknown side be b. Then 5² + b² = 13², so 25 + b² = 169, giving b² = 144 and b = 12 cm. Area = ½ × 5 × 12 = 30 cm². The 12 cm side is a length, not an area; keep the units consistent.
Traps that cost marks
- Using the diameter instead of the radius in circle formulae.
- Applying Pythagoras to a triangle that is not right-angled.
- Choosing the wrong trigonometric ratio because the sides were labelled from the wrong angle.
- Confusing perimeter (1D, cm) with area (2D, cm²) and volume (3D, cm³).