Cambridge IGCSE Additional Mathematics · Syllabus 0606 · Circular Measure
Sector Area
What is Sector Area?
The area of the pie-shaped region of a circle enclosed by two radii and the arc between them, equal to one half of the radius squared multiplied by the central angle in radians, written A = one half r squared theta. Because it is an area it carries square units such as square centimetres. Like the arc-length formula it follows from taking the fraction theta over 2 pi of the whole disc, it is not supplied in the examination formula list, and it is invalid unless the angle is in radians.
This definition is part of the Circular Measure chapter in Cambridge IGCSE Additional Mathematics.
Common mistakes with Sector Area
- Using \(\tfrac12r^2\theta\) with \(\theta\) in degrees. Why it fails Same cause, same factor. The sector area comes out about \(57.3\) times too large, and will usually exceed \(\pi r^2\) — a region bigger than the circle containing it. Fix Convert first; then compare the answer with \(\pi r^2\).