Answer:
Area shaded portion = 30π - 9√3 units²
Explanation:
The area of shaded portion = Area semi-circle + area shaded segment
∵ Area semi-circle = 1/2 πr²
∵ The diameter = 12 ⇒ radius = 6
∴ Area semi-circle = 1/2(6)²π = 18π units²
∵ The area shaded segment = area sector - area Δ
∵ The height of the non shaded portion = 3
∴ The central angle of the segment = 2cos^-1(3/6) = 2/3 π (120°)
∵ Area Δ = 1/2 r² sinФ = 1/2 (6)² sin(2/3)π = 9√3 units²
∵ Area sector = 1/2 r²Ф = 1/2 × (6)² × (2/3)π = 12π units²
∴ Area segment = 12π - 9√3 units²
∴ Area shaded portion = 18π + 12π - 9√3 = 30π - 9√3 units²