Question

A regular hexagon is inscribed in a circle of radius 2r. Then 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 length of each side of the regular hexagon is exactly equal to the radius of the given circle.

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

Perimeter of the regular hexagon = 6a

⇒ 6*2r

= 12r

So, the perimeter if the regular hexagon is 12r.

Answer.

Answer 2

Hello Dear.

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

∵ Radius of the Circle in which the Regular Hexagon is Inscribed = 2r units.

∴ Length of the one Side of the Regular Hexagon = 2r units.

Now,
∵ Perimeter of the Regular Hexagon is given by the Formula,

Perimeter = 6 × Length of One Side of Regular Hexagon.
∴ Perimeter = 6 × 2r
⇒ Perimeter = 12r units.


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


Hope it helps.