Find the area of r = 4/(1-cos θ)
sorry. This a parabola, so unless you care to restrict the domain in some way, the "area" is infinite.
Once you decide on that, recall that the area
a = ∫[θ1,θ2] 1/2 r^2 dθ
Once you decide on that, recall that the area
a = ∫[θ1,θ2] 1/2 r^2 dθ