Answer:
Area segment = (3/2)π - (9/4)√3 inches²
Explanation:
∵ The hexagon is regular
∴ Then it consists of 6 equilateral triangles with side length 3"
∴ the radius of the circle = the side of the triangle = 3"
∵ The measure of each angle of the triangle is π/3
∴ Area each triangle = (1/4)(3)²√3 = (9/4)√3
∵ Area segment = area sector - area triangle
∵ Area sector = (1/2)r²Ф
∵ r = 3" and Ф = π/3 ⇒ (60° = π/3 rad)
∴ Area sector = (1/2)(3)²(π/3) = (3/2)π
∴ The area of the segment = (3/2)π - (9/4)√3 inches²