# Circle: Area and Perimeter

### Area and Sector

#### Area of A Circle

$$A = \pi\times r^2$$

$$\pi = \dfrac{22}{7} = 3.14$$

$$A =\dfrac{1}{4} \pi\times d^2$$

$$\pi = \dfrac{22}{7} = 3.14$$

#### Area of A Sector

$$\text{Area of sector} = \dfrac{1}{2}\times r^2 \times \theta$$

$$\theta$$ in radian

$$\text{Area of sector} = \dfrac{\theta}{360^\circ}\times \pi\times r^2$$

$$\theta$$ in degree

#### Circumference of A Circle

$$\text{circumference of circle} = 2\times \pi\times r$$

$$\pi = \frac{22}{7} = 3.14$$

$$r = \text{radius}$$

$$\text{circumference of circle} =\pi\times d$$

$$d = \text{diameter}$$

#### Arc Length

$$\text{If θ is measured in degrees then:}$$

$$\text{Arc length} = \frac{\theta}{360^\circ} \times \text{circumference of circle}$$

$$\text{Arc length} = \frac{\theta}{360^\circ} \times 2\times \pi \times r$$

$$\text{If θ is measured in radians then:}$$

$$\text{Arc length} = \theta \times r$$

$$1 \pi \text { radians} = 180^\circ$$

$$1 \text{ radians ≈ 57.3°}$$