What is the area of the segment formed by a chord in a circle of radius 12 cm, if the angle subtended at the center is 150°?

Correct option is A

Given :

Radius of circle: r = 12 cm

Central angle subtended by the chord: $$\theta = 150^\circ$$​​

Formula Used :

​$$\text{Sector Area} = \frac{\theta}{360^\circ} \pi r^2$$​​

​$$\text{Triangle Area} = \frac{1}{2} r^2 \sin \theta$$​​

​$$\text{Segment Area} = \text{Sector Area} - \text{Triangle Area}$$​​
Solution :

$$\text{Sector Area} = \frac{150}{360} \pi (12)^2 \\ \ \\= \frac{5}{12} \pi \times 144 = 60\pi\\ \ \\\text{Triangle Area} = \frac{1}{2} (12)^2 \sin 150^\circ\\ \ \\\text{Triangle Area} = \frac{1}{2} \times 144 \times \frac{1}{2} \\ \ \\= 36\\ \ \\\text{Segment Area} = 60\pi - 36$$​