perimeter of a sector of the circle of area 25pi sq cm is 20 cm find the area of sector
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Answer:
25 cm²
Explanation:
Area of Circle = 25 π cm²
Area of Circle = πr²
=> πr² = 25 π
=> r² = 25
=> r = 5
Perimeter of a sector = radius + radius + Arc Length
= r + r + (θ/360)2πr
= 5 + 5 + (θ/360)10π
5 + 5 + (θ/360)10π = 20
=> (θ/360)10π = 10
=> (θ/360)π = 1
=> θ/360 = 1/π
Area of Sector = (θ/360) πr²
= (1/π)πr²
= r²
= 5²
= 25 cm²
Area of Sector = 25 cm²
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