Answer:
Area segment = 32/3 π - 16√3 inches²
Explanation:
∵ The length of the chord is 8"
∵ The length of the radius of the circle is 8"
∴ the central angle of the segment is π/3 (60° the chord and the radii
formed an equilateral triangle)
∵ The area of the segment = area the sector - area Δ
∵ Area sector = 1/2 r²Ф
∵ r = 8" and Ф = π/3
∴ Area sector = 1/2 (8²) (π/3) = 32/3 π inches²
∵ Area Δ = 1/4 s²√3
∵ The length of the side is 8"
∴ Area Δ = 1/4 (8²) √3 = 16√3 inches²
∴ Area segment = 32/3 π - 16√3 inches²