SOLUTION: Determine the area of the circle circumscribing a regular 6-pointed star if the inner regular hexagon has 25 cm on a side. Please explain.

Question 1113155: Determine the area of the circle circumscribing a regular 6-pointed star if the inner regular hexagon has 25 cm on a side. Please explain.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The 6-pointed star can be viewed as 12 equilateral triangles.

The radius of the circle circumscribing the 6-pointed star is twice the altitude of one of those triangles.

The side of each triangle is 25.
The altitude of each triangle is 25*(sqrt(3)/2).
The radius of the circumscribed circle is 25*sqrt(3).
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