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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

• Solution

• Transcript

The correct answer is option (b) 6r

Explanation:

We know that a hexagon contains six equilateral triangles, where one of the vertices of each equilateral triangles meet 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 the hexagon is equal to the radius of the hexagon.

"hello bacho hi i'm devdaval tutor at leader learning i teach maths and science and i love this two subjects so today we have a question from mats our regular hexagon is inscribed in a circle of radius r the perimeter of the regular hexagon is so we have to find out the regular hexagon perimeter out of this four option a b c and d so we have the hexagon here okay of the hexagon here i've just drawn the hexagon with the center o okay with the center o with a perpendicular m with a 90 degree angle m is 90 degree and angle a and b are the piece i have taken here now we know that a hexagon is having a six equilateral triangle means this all angle will be of 60 degree each this angle will be of 60 degree each and all the same so this is the this is one two three four five and six so all six ang equilateral triangles will be having all of the angle as 60 degree okay so it means that this all angles are off or the triangular of equilateral triangle so we we can say that as hexagon contains six equilateral triangles where one of the vertices of each equilateral triangle meet the center of the hexagon like here the its meeting on the center of the hexagon okay the vertices are meeting at the center of the hexagon okay so the radius of the smallest which is inscribing the hexagon is equal to the size of the equilateral triangle okay it's equal to the side of the equilateral triangle now therefore the perimeter right we have to find out the perimeter right so therefore the perimeter of a regular of a regular hexagon is 6 r as as y as each side of hexagon is equal to the radius the radius of what of the hexagon so we have a answer here so the answer is six are option p is the and sub simply is the correct option so i hope you like this video if you have any doubt or question you may comment in the comment section so yeah if you have liked this video do subscribe see you soon in leader classes have a great day ahead thank you for watching this video take care of yourself bye bye "

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