Question

A regular hexagon is inscribed in a circle of radius 2r. The perimeter of the regular hexagon is??

Answer 1

Solution :-

Given -

Radius of the circle = 2r

A regular hexagon inscribed in a circle is made up of 6 equilateral triangles, each having a central angle of 60°. It means that the length of each side of the regular hexagon is exactly equal to the radius of the circle, in which the hexagon is inscribed.

Hence, length of each side of the regular hexagon = 2r

Perimeter of the regular hexagon = 6a

⇒ 6*2r

= 12r

So, perimeter of the regular hexagon is 12r units.

Answer.

Answer 2

Hello Dear.


We know, the Length of Each Side of the Regular Hexagon inscribed in a circle is always equals to the Radius of the Circle.

∵ Radius of the Circle in which Hexagon is inscribed = 2r

∴ Length of One Side of the Hexagon = 2r

Now,
∵ Perimeter of the Regular Hexagon is given by the Formula,
 Perimeter = 6 × Length of 1 Side.
∴ Perimeter of the Regular Hexagon = 6 × 2r
   = 12r. units.


Hence, the Perimeter of the Hexagon which is Inscribed in the Circle of Radius 2r is 12r units.

______________________


∴ Hope it helps.