area of circle = pi r^2 = 78.54
r^2 = 78.54 / pi = 25
r = 5 inches
Each line from centre of the circle to a point on the hexagon = 5 ins
so consider one of the 6 congruent triangles formed from these lines:-
Vertex angle = 60 degrees
sin 30 = 0.5s / 5 (where s = one side of the hexagon).
0.5s = 5*0.5 = 2.5
s = 2.5 / 0.5 = 5
So the perimeter of the hexagon is 6*5 = 30 inches
