Page 3 - Lesson note-Area of sector,length of Arc

When the angle of the sector is 2π, area of the sector i.e. the whole circle = πr 2

2
2
When the angle is 1, the area of the sector = πr /2π = r /2
So, when the angle is θ, area of the sector = θ × r /2
2
A = l /r × r /2
2
A =

Perimeter of a Sector

The formula for the perimeter of the sector of a circle is given below :

Perimeter of sector = radius + radius + arc length

Perimeter of sector = 2 radius + arc length

Therefore,

Perimeter of a Sector = 2 Radius +

unless stated otherwise
Use t

Example 1- If the angle of the sector with radius 4 units is 45°, then find the area
and the length of the sector.

Solution- Area = θ/360° × πr 2

= 45°/360° × 22/7 × 4 × 4

= 44/7 square units
The length of the same sector = θ/360° × 2πr

l = 45°/360° × 2 × 22/7 × 4
l = 22/7

Example 2- A circular arc whose radius is 12 cm, makes an angle of 30° at the
centre. Find the perimeter of the sector formed. Use π = 3.14.

Solution- Given that r = 12 cm,

θ = 30° = 30° × (π/180°) = π/6

Perimeter of sector is given by the formula;

P = 2 r + r θ

P = 2 . 12 + 12 . π/6

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