Find the area of the shaded portion in the circle.

Area shaded portion = 30π - 9√3 units²

Step-by-step 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

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step-by-step explanation: