A sector occupies the fraction 2pi of a circle, so A= 2pipi r2= 12r2theta. Recall this formula; it is not supplied. For 0<theta<pi, the minor segment between chord AB and the minor arc is the sector minus triangle OAB: A_ segment= 12r2theta- 12r2sintheta. This follows by subtracting areas, so do not use a degree value in the sector term. With r=6 and theta= 3, the sector area is 6pi cm2, the triangle area is 9 3 cm2, and the minor segment area is (6pi-9 3) cm2. For a major segment, subtract the minor segment from pi r2. For a segment perimeter, add its arc and chord, not the two radii.

A sector occupies the fraction \(\dfrac\theta{2\pi}\) of a circle, so \(A=\dfrac\theta{2\pi}\pi r^2=\dfrac12r^2\theta\). Recall this formula; it is not supplied.

For \(0<\theta<\pi\), the minor segment between chord \(AB\) and the minor arc is the sector minus triangle \(OAB\): \(A_{\rm segment}=\dfrac12r^2\theta-\dfrac12r^2\sin\theta\). This follows by subtracting areas, so do not use a degree value in the sector term.

With \(r=6\) and \(\theta=\dfrac\pi3\), the sector area is \(6\pi\text{ cm}^2\), the triangle area is \(9\sqrt3\text{ cm}^2\), and the minor segment area is \((6\pi-9\sqrt3)\text{ cm}^2\).

For a major segment, subtract the minor segment from \(\pi r^2\). For a segment perimeter, add its arc and chord, not the two radii.

Sector and segment areas

Sector and segment areas