Question

A regular hexagon is inscribed in a circle, the diameter of the circle is d; what is the circumference of the hexagon ?

Answer 1

3d

Explanation:

A regular hexagon has six equivalent triangles, each triangle having one side of that of the hexagon. if the diameter of the circle in which the hexagon is inscribed is d , then its radius will be

`r=(d)/(2)`

this radius also happens to be one of the side of the equivalent triangle whose one side is also the side of hexagon. since length of one side of hexagon is

`(d)/(2)`

the circumference of the hexagon will be
`6 ((d)/(2) )\\\\thus \\circumference   \\of \\hexagon = 3d`