Question

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

• A. $3r$
• B. $6r$
• C. $9r$
• D. $12r$

Answer 1

The correct option is B

$6r$

Regular hexagon:

A regular hexagon is a closed shape polygon that has six equal sides and six equal angles.

Properties of a regular hexagon

• It has $6$ equal sides and 6 equal angles.
• It has $6$ vertices.
• The Sum of interior angles equals $720°$.
• The Interior angle is $120°$ and the exterior angle is $60°$.
• It is made up of six equilateral triangles.
• $9$ diagonals can be drawn inside a regular hexagon.

• All the sides opposite to each other are parallel.

We know that a hexagon contains six equilateral triangles, where one of the vertices of each equilateral triangle meets at the centre of the hexagon. The radius of the smallest which is inscribing the hexagon is equal to the sides of the equilateral triangle. Therefore, the perimeter of a regular hexagon is $6r$, as each side of hexagon is equal to the radius of the hexagon.

Hence,option (B) is correct answer.