area of minor segment

Area of the minor segment

= Area of the sector − Area of the triangle

= \frac{θ}{360 °} \times π r^{2} - \frac{1}{2} \times 2 r \sin \frac{θ}{2} \times r \cos \frac{θ}{2}, where θ is the angle subtened by the chord at the centre = \frac{θ}{360 °} \times π r^{2} - \frac{1}{2} r^{2} s i n θ