GCSE Mathematics · Edexcel 1MA1 · Topic G.2

Mensuration and calculation

Key points

Area: rectangle $lw$ , triangle $\frac{1}{2}bh$ , parallelogram $bh$ , trapezium $\frac{1}{2}(a + b)h$ , circle $\pi r^2$ . Circumference $C = 2\pi r = \pi d$ .
Arcs and sectors: arc length $= \frac{\theta}{360} \times 2\pi r$ , sector area $= \frac{\theta}{360} \times \pi r^2$ .
Volume: prism = area of cross-section × length; cylinder $\pi r^2 h$ ; cone $\frac{1}{3}\pi r^2 h$ , sphere $\frac{4}{3}\pi r^3$ , pyramid $\frac{1}{3} \times$ base area × height (cone and sphere formulae are given when needed).
Pythagoras: $a^2 + b^2 = c^2$ in a right-angled triangle, with $c$ the hypotenuse.
Trigonometry: SOHCAHTOA; know exact values such as $\sin 30^\circ = \frac{1}{2}$ , $\cos 45^\circ = \frac{\sqrt{2}}{2}$ , $\tan 60^\circ = \sqrt{3}$ .
Non-right-angled triangles (higher): sine rule $\frac{a}{\sin A} = \frac{b}{\sin B}$ , cosine rule $a^2 = b^2 + c^2 - 2bc\cos A$ , area $= \frac{1}{2}ab\sin C$ .
Bearings are measured clockwise from north and written with three figures, e.g. 045°.

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Mensuration is measuring and calculating: perimeter, area, volume and surface area, Pythagoras' theorem, trigonometry and bearings. Higher tier adds sectors, the sine and cosine rules and problems in three dimensions. Questions give you the…

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