Figure 1 shows a sector AOB of a circle with centre O and radius r cm. The angle AOB is θ radians. The area of the sector AOB is 11 cm^2. Given that the perimeter of the sector is 4 times the length of the arc AB, find the exact value of r.
P = 2r + rθ
we know that P = 4x rθ
and that the area A = 0.5 r2 x θ
so 0.5 r2 x θ = 11
now you can find r and θ