The perimeter of a sector of a circle of radius 14cm is 68cm. Find the area of the sector.
Answers
Answer:
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+lP=2r+l
68=2(14)+l68=2(14)+l
l=68-28l=68−28
l=40l=40
The length of arc is 40 cm.
The formula of length of arc is l=\frac{\theta}{360}\times 2\pi rl=
360
θ
×2πr
40=\frac{\theta}{360}\times 2\times\frac{22}{7}\times 1440=
360
θ
×2×
7
22
×14
40=\frac{\theta}{360}\times 8840=
360
θ
×88
\theta=\frac{40\times 360}{88}θ=
88
40×360
\theta=\frac{3600}{22}θ=
22
3600
The area of the sector is A=\frac{\theta}{360}\times \pi r^2A=
360
θ
×πr
2
A=\frac{\frac{3600}{22}}{360}\times\frac{22}{7}\times 14\times 14A=
360
22
3600
×
7
22
×14×14
A=280\ cm^2A=280 cm
2
Therefore, the area of the sector is 280 cm².