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Mensuration is the measurement of geometric figures — their lengths, perimeters, areas, surface areas and volumes. Pythagoras' theorem and trigonometry extend this to right-angled triangles.
| Shape | Perimeter | Area |
|---|---|---|
| Rectangle | 2(l + w) | l × w |
| Triangle | a + b + c | (1/2) × b × h |
| Parallelogram | 2(a + b) | b × h (perpendicular height) |
| Trapezium | a + b + c + d | (1/2)(a + b) × h |
| Circle | 2πr = πd | πr² |
π ≈ 3.14159… — leave answers in terms of π unless asked for a decimal.
Example: Area of a trapezium with parallel sides 8 cm and 12 cm, height 5 cm: = (1/2)(8 + 12) × 5 = (1/2) × 20 × 5 = 50 cm²
Circumference: C = 2πr = πd Area: A = πr²
Example: A circle has radius 7 cm. Circumference = 2 × π × 7 = 14π ≈ 43.98 cm Area = π × 49 = 49π ≈ 153.94 cm²
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