Area Related to Circles Chapter Notes - Mathematics (Maths) Class 10

Area of Sector

Sector: Sector of a Circle is given as part of Circle enclosed by 2 radius and arc.

In the diagram, shaded area OAB is the sector.
Here, θ is the angle subtended by the arc AB on the center O of the circle.

Area of the Sector is given as  

Proof:

In whole circle, the angle θ will he 360°
Area of Circle = πr²
Using Unitary Method
Area represented by 360° = πr²
Area represented by

 Area of Semi Circle

Semi-Circle is a sector forming an angle 180° with center.
θ=180°
Now, Area of Semi Circle will be given as

Area of the Semi-Circle = πr²/2

Area of Quarter Circle

Now, Area of Quarter Circle will be given as
 

Area of Quarter Circle =πr²/4

Area of Segment

Segment is defined as area enclosed by chord and arc of the circle.

In the diagram Shaded portion represents Segment AMB

Area of Segment AMB = Area of Sector OAB- Area of triangle AOB

Perimeter of Sector

• It is the length which enclosed the sector.
• Length of arc AB + OA + OB.
• OA=OB=r, that is radius of sector.

So,

perimeter of a Sector = l + 2r
Here l is length of arc and