By Team Aakash Byju's | 15th November 2022
A sector of a circle of radius 5.6 cm has a perimeter of 27.2 cm. Its area is:
l
A sector with a perimeter of 27.2 centimetres and a part of a circle of radius 5.6 centimetres has an area of approximately 44.8 square centimetres.
l
The perimeter of sector OAB = 27.2 cm The area of sector OAB ≈ 44.8 cm.
l
2
Let us assume that l is the length of the arc AB that forms a sector OAB. So, the perimeter of the sector OAB is
l
Perimeter OAB = length of OA + length of OB + length of the arc AB
From the given data we can write, Length of the arc AB = = 27.2 - (5.6+5.6) = 16 centimetres.
l
Arc length is also expressed in terms of the angle subtended by the arc at the centre of the circle.
l
l = rθ
=> θ =
l
r
=
16
5.6
radian
But we need to convert this into degrees, we get
l
θ =
5.6
(
(
∵ 1 radian = 180 where π =
16
180
π
7
)
(
π
22
θ =
16
5.6
(
(
180
=> θ ≈ 163.63 degrees.
7
22
Now, let us find the area of the sector using the formula
Area of sector
( in degrees)
360
2
(
(
=
πr
θ
l
Substituting the values in the above equation
Area of OAB =
163.63
360
(
22
7
(
(
5.6
(
2
=
Area of OAB ≈
44.8 cm
2
l