Verified answer

11θ = π

θ = π/11

One loop goes from θ = 0 to θ = π/11.

dA = (1/2) r^2 dθ = (1/2) 16 sin^2 (11θ) dθ from θ = 0 to θ = π/11.

A = ∫ (1/2) 16 sin^2 (11θ) dθ = 1.142397329... ≈ 1.142

The curve r = sin(theta) is a circle of diameter a million and it has section is pi/4 Your curve is compressed through aspect 8 in angular route and for this reason the part of one loop of your curve is 8 situations smaller answer: section = pi/32