r = 4 + 3 sin 𝜃

Answer 1

It is shaded entirely right of the y axis

Answer 2

since we are looking at the region where -π/2 ≤ θ ≤ π/2 we have
a = ∫[-π/2,π/2] 1/2 r^2 dθ
= ∫[-π/2,π/2] 1/2 (4+3sinθ)^2 dθ = 41π/4