The area of a regular n-sided polygon circumscribed about a circle of the radius R is equal to
= ..
The area of circle of the radius R is S = .
The ratio you are asking for is =
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website! = radius of the circle = height of each of the 6 triangles forming the hexagon. = area of the circle = area of the hexagon is the ratio asked for.
You may have a formula to calculate the area of a regular hexagon
as a function of its apothem (which in this case is R),
but I calculated it by figuring the sides and area of the triangles.
The angles of those triangles measure .
That makes for the triangles,
so .
Area for 1 triangle would be ,
and the area of the hexagon is 6 times that .