This module covers the measurement skills that turn up in mensuration questions: finding the area and perimeter of compound shapes, converting between square units, separating arc length from sector area, finding the surface area of prisms and cylinders, and checking that an answer is the right kind of quantity.
Check the current Cambridge IGCSE Mathematics 0580 syllabus for the exact wording and the Core or Extended content in your exam year. Our Mathematics learning guide shows where this module sits among the others.
What should you already know?
You should know the area of a rectangle, triangle and circle, and the circumference of a circle. You should also be comfortable with rounding to 3 significant figures and with the metric units of length. Reading precision, bounds and measurement first helps if rounding still feels uncertain.
An orienting example
A sector has radius 9 cm and angle 140°. Find its perimeter.
The perimeter is the arc plus two radii.
Arc = 140/360 × 2π × 9 = 21.99 cm. Add 9 + 9 = 18. Perimeter = 39.99, so 40.0 cm (3 s.f.).
That one question uses a fraction of a circle, a choice between length and area formulas, and the edges that belong to the boundary. The lessons below take each idea apart.
In what order should you study the lessons?
- Decompose a compound shape: cut a figure into known pieces and count only the outside edge for perimeter.
- Calculate area after converting units: learn why area conversions use the squared factor.
- Distinguish arc length from sector area: keep the curved-length and region formulas apart.
- Unfold a prism to find surface area: use a net so no face is missed.
- Check an area answer using dimensions: finish with a check you can apply to every other lesson.
Then try the mixed practice set, which blends all five skills. The non-calculator working trainer is a useful companion for the arithmetic.
What are the common traps?
- Counting an inside edge in the perimeter. A cut line or a shared side is not on the boundary.
- Converting area with the length factor. 1 m² is 10 000 cm², not 100 cm².
- Mixing arc length and sector area. One uses 2πr, the other πr².
- Using the diameter as the radius. Read whether a circle shows its radius or diameter.
- Missing a face. A prism has two ends, and a box without a lid has five faces.
- Rounding too early. Keep full values in the calculator and round the final answer.
How should you use the practice set?
Attempt each question on paper before opening the answer. After each one, circle the step where you were unsure. Use the routing table at the end of the practice set to choose the lesson to revisit, and record repeated errors in the mistake log and retest queue.
If you want a teacher to look at your own working and not just the model answers, our online one-to-one Mathematics tuition starts with a paid one-hour trial lesson.