Question

If the perimeter of a sector of a circle of radius 6.5 cm is 29 cm, then its area is
(a)58 cm²
(b)52 cm²
(c)25 cm²
(d)56 cm²

Answer 1

Answer:

The Area of sector of a circle is 52 cm² .

Among the given options option (b) 52 cm² is the correct answer

Step-by-step explanation:

Given :  

Perimeter of a sector of a circle,P = 29 cm

Radius of a circle = 6.5 cm

Perimeter of the sector ,P = length of the arc + 2×  radius

P = θ/360° × 2πr + 2r

29 = θ/360° × 2 × 22/7 × 6.5 + 2 × 6.5

29 = θ/360° × 44/7 × 6.5 + 13  

29 - 13  = θ/360° × 286/7

16 = θ/360° × 286/7

θ/360° = 16 × 7/286

θ/360° = 112/286 ……(1)

Area of sector of a circle, A = θ/360° × πr²

A = (112/286) × 22/7 × 6.5 × 6.5

[From eq 1]

A = 676/13

A = 52 cm²

Area of sector of a circle = 52 cm²

Hence, the Area of sector of a circle is 52 cm²

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Solution:

Let r, l are radius and length

of an arc of a sector .

1) perimeter (P) = 29 cm [given]

=> l+2r = 29

=> l = 29 - 2r

=> l = 29 - 2×6.5 [r=6.5cm ]

=> l = 29 - 13

=> l = 16 ----(2)

2)Area of the sector( A )= lr/2

= (16 × 6.5 )/2

= 8 × 6.5

= 52 cm²

Therefore,

Option (b) is correct.

•••