SOLUTION: A regular hexagon is inscribed in a circle whose diameter is 20 m. find the area of the 6 segments of the circle formed by the sides of the hexagon.

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Question 1178373: A regular hexagon is inscribed in a circle whose diameter is 20 m. find the area of the 6 segments of the circle formed by the sides of the hexagon.
Answer by MathLover1(20850) About Me  (Show Source):
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a circle whose diameter is d=20m=> radius is r=10m
A%5Bc%5D+=r%5E2%2Api=10%5E2%2Api=314.16

A regular hexagon is inscribed in circle of radius+r. The perimeter of regular hexagon is 6r=> side is equal to radius
A%5Bh%5D=+%283sqrt%283%29%2As%5E2%29%2F+2 where s is the length of a side of the regular hexagon
s+=10
A%5Bh%5D+=+%283sqrt%283%29%2A10%5E2%29%2F+2+=259.81
The area of the 6+segments of the circle formed by the sides of the hexagon is
314.16-259.81=54.35sq. m