Question 42824
You can use trig to do this...
Make a triangle with the segment connecting the midpoints of the sides as the base...
Then bisect the top angle and drop an altitude, making two right triangles...
Each right triangle has a top angle of 67.5 degrees...the long leg is 9, which is half of the 18...the hypotenuse is half the side of the hexagon...
Thus sin 67.5 = 9/x and
x = 9 / (sin 67.5) = 9.74
and the side is double that, or about
19.48 inches