The shaded area below has a area of 4pi. Find the perimeter of the sector.
We first find the radius,
Let r be the radius.
\(\dfrac{40^\circ}{360^\circ} \cdot \pi r^2 = 4\pi\\ r = 6\)
Then we can use the formula \(P = \dfrac{\theta}{360^\circ} \cdot \left(2\pi r\right) + 2r\) to calculate the perimeter of the sector.
I believe you can finish it on your own.