Question

The perimeter of a sector of a circle of radius 14 cm is 68 cm. Find the area of the sector. ( Ans. is 280 cm)​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The area of the sector is 280 cm².

Step-by-step explanation:

Given : The perimeter of a sector of a circle of radius 14 cm is 68 cm.

To Find : The area of the sector ?

Solution :

Perimeter of a sector = Twice of radius + length of arc

i.e. $P=2r+l$

$68=2(14)+l$

$l=68-28$

$l=40$

The length of arc is 40 cm.

The formula of length of arc is $l=\frac{\theta}{360}\times 2\pi r$

$40=\frac{\theta}{360}\times 2\times\frac{22}{7}\times 14$

$40=\frac{\theta}{360}\times 88$

$\theta=\frac{40\times 360}{88}$

$\theta=\frac{3600}{22}$

The area of the sector is $A=\frac{\theta}{360}\times \pi r^2$

$A=\frac{\frac{3600}{22}}{360}\times\frac{22}{7}\times 14\times 14$

$A=280\ cm^2$

Therefore, the area of the sector is 280 cm².

#Learn more

A rhombus has a perimeter of 68 cm and diagonal of 30 cm . Find the area of the rhombus.

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