Question

A Sector Of Radius 4.2 Has An Area 9.24 Cm2 .Find Its Perimeter.

Answer 1

Answer:

Perimeter is 12.8 cm.

Step-by-step explanation:

Given:

Area of the Sector = 9.24 cm²

Radius of the circle, r = 4.2 cm

To find: Perimeter of the sector.

let $\theta$ be the angle of subtended at center of the sector.

We know that,

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

$9.24=\frac{\theta}{360}\times\frac{22}{7}(4.2)^2$

$9.24\times360=\theta\times22(0.6)(4.2)$

$3326.4=\theta\times55.4$

$\theta=\frac{3326.4}{55.44}$

$\theta=60^{\circ}$

Length of the arc = $\frac{\theta}{360}\times2\pi r$

                             $=\frac{60}{360}\times2(\frac{22}{7})(4.2)$

                             $=\frac{1}{6}\times2(22)(0.6)$

                             $=44(0.1)$

                             $=4.4$

Perimeter of the Sector = Length of the arc + 2 × Radius

                                       = 4.4 + 2 × 4.2

                                       = 4.4 + 8.4

                                       = 12.8 cm

Therefore, Perimeter is 12.8 cm.

Answer 2

Answer:

answer is:

perimeter: 12.8