Given the circular sector in radians and a total perimeter of 20?

Question

1. Express r as a function of theta
2. Express the area A of the sector as a function of theta

http://img176.imageshack.us/img176/682/circlesn5.jpg

Thanks

Answer 1

1. Arc = r

Perimeter = arc + 2r = 20
Thus rθ + 2r = 20
r(θ + 2) = 20
So r = 20/(θ + 2)

2. Area = ½ r²θ

Thus Area = ½ [20/(θ + 2)]² * θ
= 200θ/(θ + 2)²

Answer 2

1. r(θ) = R
2. A = (1/2)(r^2)θ

Answer 3

1.
s = (theta) r
or, 20 = (theta) r
or, r = 20/(theta)

2.
A = (theta)/2 * r^2
or, A = (theta)/2 * (20/theta)^2
or, A = 400/2 * (theta)
or, A = 200 (theta)