What is the formula for calculating the area of a sector?

The formula for calculating the area of a sector is derived from the formula for the area of a circle. A sector represents a portion of the circle defined by a central angle, θ, measured in degrees. The total area of a circle is given by πr², where r is the radius.

To find the area of a sector, we take the fraction of the circle that corresponds to the angle θ. Since the whole circle corresponds to an angle of 360 degrees, the area of the sector can be calculated as a fraction of the total area of the circle:

Area of sector = (θ/360) × Total area of the circle.

Substituting the formula for the area of the circle into this expression gives:

Area of sector = (θ/360) × πr².

This shows that the correct option is the one that represents this relationship accurately, confirming that the formula is indeed Area = (θ/360) × πr². This understanding is essential when applying the concept of sectors in various geometric problems.