Part of the stage decoration is a "fan" shape and is to be covered with a white cloth. If the radius of the fan is x+3 and its area is 198 meter squared, what is the dimension of the fan?

Answer 1

The fan is a sector of a circle. That means that

198 = 1/2 (x+3)^2 θ

Unless you know how much of a circle the fan occupies (that is, what is θ, compared to 2π), there's no way to solve for x.

If the fan is a half-circle, θ=π, so

198 = 1/2 (x+3)^2 (π/2)
(x+3)^2 = 198*4/π = 252.10
x+3 = 15.88
x = 12.88

Now use that to decide what the "dimension" is.

Answer 2

oops - I plugged in π/2 instead of π.

The solution above is correct if the fan is 1/4 of a circle.