Area of a sector subtending angle θ (deg) at the centre of a circle of radius r is:

To find the area of a sector of a circle, we follow these steps: 1. **Total Area**: The total area of a circle with radius $r$ is given by the formula: $$A_{total} = \pi r^2$$ 2. **Total Angle**: A complete circle subtends an angle of $360^\circ$ at its center. 3. **Proportionality**: A sector is a fraction of the entire circle. The ratio of the area of the sector to the total area of the circle is the same as the ratio of the angle subtended by the sector ($\theta$) to the total angle of the circle ($360^\circ$). $$\frac{\text{Area of Sector}}{\text{Total Area}} = \frac{\theta}{360^\circ}$$ 4. **Derivation**: Multiply both sides by the total area: $$\text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2$$ Thus, the area of the sector is $(\theta/360) \times \pi r^2$.