Area, perimeter, arcs and sectors
Standard shape formulas (memorise)
| Shape | Area | Perimeter |
|---|---|---|
| Square (side a) | a² | 4a |
| Rectangle (l × w) | lw | 2(l + w) |
| Triangle (base b, height h) | ½ × b × h | sum of sides |
| Parallelogram (b × h) | bh | sum of sides |
| Trapezium | ½(a + b) × h | sum of sides |
| Circle (radius r) | πr² | 2πr (circumference) |
Sector and arc of a circle
A sector is a "pie slice" of a circle bounded by two radii and an arc.
For a sector with angle θ° (at the centre):
- Arc length = (θ / 360) × 2πr
- Sector area = (θ / 360) × πr²
The fraction θ/360 is the fraction of the full circle.
Example: r = 10 cm, θ = 72°. Arc length = (72/360) × 2π × 10 = 0.2 × 20π = 4π ≈ 12.57 cm. Sector area = (72/360) × π × 100 = 0.2 × 100π = 20π ≈ 62.83 cm².
Perimeter of a sector
Perimeter = 2 × radius + arc length = 2r + (θ/360) × 2πr.
Don't forget the two radii — a common slip costs A1.
Composite shapes
Break into rectangles, triangles, semicircles, etc. Add or subtract areas. Carefully track which lengths are missing — use the sum of opposite sides.
Units
Length: cm, m. Area: cm², m². Be consistent. If asked for the perimeter and the diagram is in m but radii in cm, convert before adding.
Common CCEA exam tip
Leave answers in terms of π only if the question asks. Otherwise round to 3 significant figures (or 1 decimal place if specified). Include units — a missing unit can lose the final A1 mark.
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