Answer:
the ratio of the area of the hexagon vs area of the circle that contains it is 0.8269
Explanation:
The area of a hexagon Ah expressed in terms of the distance from the centre to one of the vertex R is
Ah= 6* (area triangle with angle 2π/6) = 6* (1/2)*R*R sin (2π/6) = 3*R²*√3/2 =
(3/2)√3*R²
the area of the circle Ac that contains such hexagon is
Ac= π*R²
the ratio of the area of the hexagon vs area of the circle is
r= Ah/Ac = (3/2)√3*R²/(π*R²) = 3*√3/(2*π) = 0.8269
