Area of a sector formula: area = θ/360 × πr²
The area of a sector formula is area of a sector = (θ/360) × πr², with θ in degrees.
What each letter means
- \(r\) the radius
- \(\theta\) the angle at the centre, in degrees
When to use it
To find the area of a 'slice' of a circle. Subtract the triangle ½r² sin θ to get the area of a segment.
Worked example
Find the area of a sector of radius 7.5 cm and angle \(72^\circ\).
- \(\dfrac{72}{360}\times\pi\times7.5^2=0.2\times56.25\pi\)
Answer: \(35.3\text{ cm}^2\) (3 s.f.)
Common mistake
Using 2πr (the circumference) instead of πr² (the area).
On your course
| Course | In the exam |
|---|---|
| Edexcel 4MA1 (Higher) | Not given: learn it |
| Cambridge 0580 | Not given: learn it |
From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).
Practise and revise
Questions
What is the area of a sector formula?
The area of a sector formula is area of a sector = (θ/360) × πr², with θ in degrees. r: the radius; θ: the angle at the centre, in degrees.
Is the area of a sector given in the exam?
Edexcel 4MA1 (Higher): not given: learn it. Cambridge 0580: not given: learn it. This comes from our own IGCSE Maths formula sheets; your teacher has the official booklet.
What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc, like a slice of pizza. A segment is bounded by a chord and an arc: sector area minus the triangle.
Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.