Question

The area of a sector whose perimeter is four times its radius r units, is
(a)$\frac{r^{2}} {4}$ sq. units
(b)2r² sq. units
(c)r²sq.units
(d)$\frac{r^{2}} {2}$ sq. units

Answer 1

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….

Answer 2

$\frac{ theta }{360} \times 2 \: \pi \: r + 2r \: = 4r \\ \\ \frac{theta}{360} \times 2\pi \: r = 2r \\ \\ \frac{theta}{\pi} = 1$

$\frac{theta}{360} \times \pi \: r {}^{2}$

$\frac{theta}{360} = 1 \\ \\ \huge \bold{area \: of \: sector = r {}^{2} }$

The area of the sector of a circle of radius r subtending an angle of θ is,