Find the area of the sector of a circle of radius r and central angle θ.

The area of the sector is the total area subtended by an arc at the center.

Answer: (θ/360)πr² is the area of the sector of a circle of radius r and central angle θ.

Explanation: 

The area of a sector can be determined by the area of a sector formula which is given by:

Area of a sector= (θ/360)πr²

Where

r = radius of a sector.

θ = an angle subtends by the arc.

Let's take an example:

The area under an arc that subtends an angle of 90º at the center of a circle with a radius of 7 units can be determined by the formula given above.

Solution:

Given, radius r = 7 units and central angle θ = 90º

Area = (θ/360)πr²

Area under an arc = (90/360) x (22/7) x 7² [taking π = 22/7]

Area = 38.5 sq. units

Thus, (θ/360)πr² is the area of the sector of a circle of radius r and central angle θ.