What is the formula used to find the area of a sector of a circle?

The formula for finding the area of a sector of a circle is A = (1/2)r²θ, where r represents the radius of the circle and θ is the angle in radians that defines the sector.

This formula is derived from the fact that the area of a full circle is given by A = πr². Since a sector represents a portion of the circle, we can find the area of the sector by taking the fraction of the full circle that the sector represents, based on its angle compared to the full circle's 2π radians.

In mathematical terms, the area of the sector can be expressed as:

A = (θ / (2π)) * (πr²).

This simplifies to:

A = (1/2)r²θ, which directly matches the correct answer.

This approach clearly shows how the area is proportional to both the square of the radius and the angle of the sector. The units of area are consistent, keeping in mind that when θ is in radians, the formulas are properly applied.