SOLUTION: Express answer in exact form. A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.

Question 384131: Express answer in exact form.
A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.
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radius of the circle = 3"
Area of circle = 9*pi
Area of hexagon = ns^2*cot(180/n)/4, n = 6, s = 3
Area of hexagon = 54*cot(30)/4 = 54sqrt(3)/4 = 13.5sqrt(3)
Difference = 9*pi - 13.5sqrt(3) for the whole circle and hexagon
Divide by 6
= 1.5*pi - 2.25sqrt(3) sq inches

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