Question

The perimeter of a sector of a circle of radius 5.2cm is 16.4cm. Find the area of the sector

Answer 1

Given :-

Perimeter of sector of circle =16.4cm

radius of circle =5.2 cm

To find

The Area of sector

Now

A.T.Q

• First find the length of arc

$\sf\implies 5.2+5.2+l=16.4\\ \\ \sf\implies 10.4+l=16.4\\ \\ \sf\implies l= 16.4-10.4\\ \\ \sf\implies l= 6cm\\ \\ \sf\:\:\:\:\: \bullet length\:of\:Arc= 6cm$

Now find the Area of sector

$\boxed{\sf{Area\:of\: sector=\dfrac{1}{2} radius\times length\:of\:arc}}$

• Where r is radius
• and l is length of arc

So find the Area

$\sf\implies Area=\dfrac{1}{\cancel2}\times 5.2\times \cancel{6}\\ \\ \sf\implies Area=5.2\times 3\\ \\ \sf\implies Area\:of\:sector=15.6cm{}^{2}$

$\boxed{\bigstar{\sf{Area\:of\: sector=15.6cm{}^{2}}}}$

Answer 2

Given: Perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm.

To find: The area of the sector.

Answer:

Let's first find the length of the arc.

Perimeter of an arc = (2 * radius) + length

Using the values we have,

16.4 = (2 * 5.2) + length

16.4 = 10.4 + length

16.4 - 10.4 = length

6 cm = length

We now have the length of the arc. Let's find the area of the sector.

$\sf Area\ of\ the\ sector\ =\ \dfrac{1}{2}\ \times\ radius\ \times\ length\ of\ the\ arc$

Using the values in it,

$\sf Area\ =\ \dfrac{1}{2}\ \times\ 5.2\ \times\ 6\\\\\\Area\ =\ 15.6\ cm^2$

Therefore, the area of the sector is 15.6 cm².