Answer:
Area shaded portion = 16/3 π - 8√3
Step-by-step explanation:
The shaded portion consists of 2 equal segment
∵ Two circles have the same radii = 4
∵ The the length of the common chord of the two circles = 4
∴ The central angle of each segment = π/3 (60° equilateral Δ)
∵ Area segment = area sector - area Δ
∵ Area sector = 1/2 r²Ф = 1/2 × (4)² × π/3 = 8/3 π
∵ Area Δ = 1/4 s² √3 = 1/4 × (4)² × √3 = 4√3
∴ Area segment = 8/3 π - 4√3
∴ Area shaded portion = 2(8/3 π - 4√3) = 16/3 π - 8√3
