Areas of Sector and Segment of a Circle

Below we will discuss the area of sector as well as the area of segment of a circle.

Area of Sector

Area of sector of a circle is determined by multiplying angle subtended by the sector and area of the circle and further dividing the result with 360°.

Formula for Area of Sector of a Circle

Formula for area of sector is given by:

Area of Sector (when θ is in degrees) = πr² × (θ / 360°)

Area of Sector (when θ is in radians) = (1/2) × θr²

Formula for Area of Major Sector of a Circle

Formula for the area of major sector of a circle is given by:

Area of Major Sector = Area of Circle – Area of Minor Sector

Area of Segment

Area of segment of a circle is given by subtracting the area of triangle from the area of the sector. From the figure below we can clearly see that the area of segment of circle is equal to the difference of area of sector and area of triangle.

Area of Segment = Area of Sector – Area of Triangle

Formula for Area of Segment of a Circle

Formula for the area of segment of a circle is given below:

Area of Segment (when θ is in radians) = (1/2) × r²(θ – sinθ)

Area of Segment (when θ is in degrees) = (1/2) × r²[(π/180)θ – sinθ]

Formula for Area of Major Segment of a Circle

Formula for the area of major segment of a circle is given by:

Area of Major Segment = Area of Circle – Area of Minor Segment

Areas of sector and segment of a circle with radius r and subtends an angle θ (in radians) are given by (1/2)×θr² and (1/2)×r²(θ -sinθ) respectively. The area of the sector and the area of the segment of the circle are easily calculated using the above formula.

In this article, we will explore the areas of sector and segment in detail and also learn the basics of sector and segment of a circle.