SOLUTION: Express the 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.
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Question 1206671: Express the 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.
(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3.)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
If you draw this, there are 6 equal equilateral triangles formed by the hexagon with sides 3. The combined area, or the area of the hexagon, is (6/4)*3^2*sqrt*(3)=13.5 sqrt(3)
The area of the whole circle is 9pi.
the area outside the hexagon is 9pi-13.5 sqrt(3)=4.89 in^2
and the exact area of each segment is 1/6 of that or (1/6)*(9pi-13.5 sqrt(3)
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