Question

Find the area of the shaded portion intersecting between the two circles.

Answer 1

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