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 )
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
L is the arc length.
R is the radius of the circle of which the sector is part.
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