Mensuration, Pythagoras and Trigonometry

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.

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Perimeter and Area of 2D Shapes

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

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Circles

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