Measurement and geometry
Measurement and geometry
Measurement questions are mostly unit conversion and formula selection. Learn the factors: 1 km = 1000 m, 1 m = 100 cm, 1 kg = 1000 g, 1 L = 1000 mL, 1 m³ = 1000 L, plus the squared and cubed versions (1 m² = 10 000 cm², 1 m³ = 1 000 000 cm³). Time needs care: 1 h 45 min = 1.75 h, not 1.45 h.
Geometry facts to have ready: perimeter is a length while area is squared; triangle area = ½ × base × perpendicular height; circle area = πr² and circumference = 2πr; volume of a prism = cross-sectional area × length. Angle rules: straight line 180°, at a point 360°, vertically opposite angles equal, alternate angles equal and co-interior angles supplementary between parallel lines, triangle sum 180°, quadrilateral 360°. Pythagoras (a² + b² = c²) applies only to right triangles, with c the hypotenuse. For similar figures, lengths scale by k but areas by k².
Traps: a diameter is given when the formula needs a radius; the triangle height must be perpendicular to the base; mixed units must be converted before calculating; and a length scale factor must be squared for area.
Worked example. A rectangular lawn 12 m by 8 m contains a circular pond of diameter 4 m. Grass area = (12 × 8) − π × 2² = 96 − 12.57 ≈ 83.4 m². The radius is 2 m, half the given diameter - using 4 m would overstate the pond by a factor of four.