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DERIVING THE FORMULA FOR THE AREA OF A SECTOR Adapted from Walch Education

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Key Concepts 3.4.2: Deriving the Formula for the Area of a Sector 2 A sector is the portion of a circle bounded by two radii and their intercepted arc.

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Key Concepts, continued 3.4.2: Deriving the Formula for the Area of a Sector 3 To find the area of a sector,, when the central angle is given in radians, we can set up a proportion using the area of a circle, We can solve this proportion for the area of the sector and simplify to get a formula for the area of a sector in terms of the radius of the circle and the radian measure of the central angle .

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Key Concepts, continued 3.4.2: Deriving the Formula for the Area of a Sector 4 To find the area of a sector when the central angle is given in degrees, we can set up a proportion using the area of a circle.

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Practice 3.4.2: Deriving the Formula for the Area of a Sector 5 A circle has a radius of 24 units. Find the area of a sector with a central angle of 30.

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Solution 3.4.2: Deriving the Formula for the Area of a Sector 6 1. Find the area of the circle. 2. Set up a proportion.

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Solution, continued 3.4.2: Deriving the Formula for the Area of a Sector 7 3. Multiply both sides by the area of the circle to find the area of the sector. The area of the sector is approximately 150.80 units 2.

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Your Turn. 3.4.2: Deriving the Formula for the Area of a Sector 8 A circle has a radius of 6 units. Find the area of a sector with an arc length of 9 units.

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Ms. Dambreville Thanks for Watching!!!!