Area Of A Sector

 

The area of a sector of a circle is given by the formula, ½ r² ∅, where r represents the radius and ∅ is the angle in radians subtended by the arc at the centre of the circle. So the shaded area in the below circle is equal to ½ r² ∅ .

If the central angle is known

Area  = π r^2 ( C/ 360 )

 where:

C  is the central angle in degrees

r  is the radius of the circle of which the sector is part.

π  is Pi, approximately 3.142

If the arc length is known

We can calculate  Area = RL/2

 where:

L is the arc length.

R is the radius of the circle of which the sector is part.

Example:

Find the area of the segment AB shown in the diagram.

Radius of the circle is 10 cm and <AOB = 120°.

In a given circle, Radius (r) = 10 cm And, ∅ = 120°

Area of segment AYB = Area of sector OAYB — Area of AOBA

Area of sector OAYB = (∅ / 360) x πr^2

= 120/360 X 22/7 X(10)^2

= 1/3 X 22/7 X(10)^2

= 22 x 10 = 220 cm2