A sector is a "pizza slice" of a circle, bounded by two radii and an arc. An arc is the curved part of the sector's boundary.
Arc length: $$L = \frac{\theta}{360} \times 2\pi r$$
Sector area: $$A = \frac{\theta}{360} \times \pi r^2$$
where $\theta$ is the angle of the sector in degrees and $r$ is the radius.
Example: Sector with radius 6 cm and angle 120°: $$\text{Arc length} = \frac{120}{360} \times 2\pi \times 6 = \frac{1}{3} \times 12\pi = 4\pi \approx 12.6\text{ cm}$$ $$\text{Sector area} = \frac{120}{360} \times \pi \times 36 = \frac{1}{3} \times 36\pi = 12\pi \approx 37.7\text{ cm}^2$$
Perimeter of a sector = arc length + 2 radii.
Common error: using the full circumference/area formula without the fraction $\frac{\theta}{360}$, or forgetting to add the two radii when finding the perimeter.