Posted by suzy on Tuesday, November 30, 2010 at 6:14pm.
draw the diagonals of the hexagon and you will have 6 equilateral triangles.
let's look at one of these.
the height can found by Pythagoras
h^2 + 9^2 = 18^2
h^2 = √243 = 9√3
so the area of one of them = (1/2)(18)(9√3) = 81√3
there are 6 of them ,so total area of hexagon = 486√3
Area of circle = π(18)^2 = 324π
area of difference = 324π - 81√3 or appr. 176.1
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