Area of Sectors

A sector takes the same share of a circle's area as its angle takes of a full turn, so \(A = \frac{\theta}{360} \times \pi r^2\). In NSW Year 8 maths (NESA outcome MA4‑ARE‑C‑01) quadrants and semicircles are the special cases with \(\theta = 90^\circ\) and \(\theta = 180^\circ\).

You will find the areas of minor and major sectors, composite shapes such as a triangle on a semicircle, and a segment as a sector minus a triangle, then work backwards to an angle or a radius. You will also compare slices from two pizzas, find the lawn wet by a sprinkler that turns back and forth, and the glass cleaned by a windscreen wiper. It is part of Year 8 Area and Perimeter.