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Area of a Sector

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The derivation of the area of a sector is presented

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Area of a Sector

1. 1. Area of a Sector by SBR www.harekrishnahub.com
2. 2. www.harekrishnahub.com Consider a circle with centre πΆ and radius π units. Let π¨ and π© be any points on the circle. The area bounded by the arc π¨π© and the two radii πΆπ¨ and πΆπ© is called the sector π¨πΆπ©. Let us find the area of the sector π¨πΆπ©.
3. 3. www.harekrishnahub.com Let the area of the sector be π¨. Let the angle subtended by the arc π¨π© at the centre of the circle be π½ (called angle of the sector). We know that in a circle, the area of the sector is proportional to the angle of the sector. Therefore, ππππ ππ ππππππ π¨πΆπ© β π¨πΆπ© = ππππ ππ ππππππ πππ π (but 360 π = 2π) β ππππ ππ ππππππ π¨πΆπ© π½ = ππππ ππ ππππππ ππ
4. 4. www.harekrishnahub.com β π¨ π½ = ππ π ππ β π¨ = π π π π π½ Therefore, the area of the sector of radius π¨ = π π π π π½