Page 3 - Lesson Note
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When the angle of the sector is 2π, area of the sector i.e. the whole circle = πr
2
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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
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A = l /r × r /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 + ×
Use = ⁄ unless stated otherwise
Example 1- If the angle of the sector with radius 4 units is 45°, then find the area
and the length of the sector.
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Solution- Area = θ/360° × πr
= 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 = 2r + r θ
P = 2 . 12 + 12 . π/6
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