The area of a sector whose perimeter is four times its radius r units, is
(a) sq. units
(b)2r² sq. units
(c)r²sq.units
(d) sq. units
Answers
Answered by
21
Answer:
The area of sector is r².
Among the given options option (c) r² sq. units is the correct answer.
Step-by-step explanation:
Given :
Perimeter of sector is four times the radius of a circle.
Perimeter of the sector ,P = θ/360° × 2πr + 2r
θ/360° × 2πr + 2r = 4r
θ/360° × 2πr = 4r - 2r
θ/360° × 2πr = 2r
2r(θ/360° × π) = 2r
(θ/360° × π) = 2r/2r
(πθ/360°) = 1 …………..(1)
Area of sector, A = θ/360° × πr²
A = πθ/360° × r²
A = 1 × r²
[From eq 1]
A = r²
Area of sector = r² sq. units
Hence, the area of sector is r².
HOPE THIS ANSWER WILL HELP YOU….
Answered by
5
The area of the sector of a circle of radius r subtending an angle of θ is,
mysticd:
Will you give different method , other than first answer.
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