Question

the perimeter of a sector of a circle of radius 4.2 cm is 12.8 find the area of the sector​

Answer 1

see down and then up

let the radius of the circle be r = 4.2 cm

let the arc length AB be p cm.

the perimeter of the sector AOB = p+2r

therefore, p+2r=12.8

p+2*4.2=12.8

p+8.4=12.8

p=12.8-8.4

p = 4.4 cm

the length of the arc = 4.4 cm

the circumference of the circle =

let the sector makes an angle θ with the center.

then see the attachment

hope this helps you.

Answer 2

Answer:

Required area is $9.24 \: {cm}^{2}$

Step-by-step explanation:

Here given,perimeter of a sector of a circle of radius 4.2 cm is 12.8 .

We know if r is the radius and l is the length of an arcthen area of the secor is

$\frac{1}{2} \times {r}^{2} \times \theta \\ = \frac{1}{2} \times r \times r\theta \\ = \frac{1}{2} \times r \times l$

Where

$l = r\theta$

Given, perimeter of the sector is 12.8 cm and r is 4.2 cm.

Therefore,

Perimeter

$= l + 2r = 12.8 \\ l + 2 \times 4.2 = 12.8 \\ l + 8.4 = 12.8 \\ l = 12.8 - 8.4 \\ l = 4.4$

Required Area of the sector is

$\frac{1}{2} \times l \times r = \frac{1}{2} \times 4.4 \times 4.2 = 9.24 \: {cm}^{2}$