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If a regular hexagon circumscribes a circle of radius r, then its perimeter is :
- a)4√3r
- b)6√3r
- c)6r
- d)12√3r
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If a regular hexagon circumscribes a circle of radius r, then its peri...
The regular hexagon which is inscribed in a circle has one side length is equal to the radius of the circle .
so, its perimeter is 6r
Most Upvoted Answer
If a regular hexagon circumscribes a circle of radius r, then its peri...
The perimeter of a regular hexagon is given by the formula P = 6s, where s is the length of each side.
In this case, the hexagon circumscribes a circle of radius r. This means that the distance from the center of the circle to each vertex of the hexagon is equal to r.
In a regular hexagon, each interior angle is 120 degrees. By drawing a line from the center of the circle to each vertex of the hexagon, we can create 6 congruent equilateral triangles.
In an equilateral triangle, each interior angle is 60 degrees. Since the line from the center of the circle to each vertex of the hexagon bisects the interior angle of each equilateral triangle, we can conclude that the measure of each angle formed by the line and the side of the hexagon is 30 degrees.
Using this information, we can draw a right triangle with one leg equal to r and the hypotenuse equal to the side length of the hexagon. By using trigonometry, we can find the length of each side of the hexagon.
sin(30 degrees) = r/s
1/2 = r/s
s = 2r
Plugging this value of s into the formula for the perimeter of the hexagon, we get:
P = 6s
P = 6(2r)
P = 12r
Therefore, the perimeter of the hexagon is 12r.
So, the correct answer is not listed.
In this case, the hexagon circumscribes a circle of radius r. This means that the distance from the center of the circle to each vertex of the hexagon is equal to r.
In a regular hexagon, each interior angle is 120 degrees. By drawing a line from the center of the circle to each vertex of the hexagon, we can create 6 congruent equilateral triangles.
In an equilateral triangle, each interior angle is 60 degrees. Since the line from the center of the circle to each vertex of the hexagon bisects the interior angle of each equilateral triangle, we can conclude that the measure of each angle formed by the line and the side of the hexagon is 30 degrees.
Using this information, we can draw a right triangle with one leg equal to r and the hypotenuse equal to the side length of the hexagon. By using trigonometry, we can find the length of each side of the hexagon.
sin(30 degrees) = r/s
1/2 = r/s
s = 2r
Plugging this value of s into the formula for the perimeter of the hexagon, we get:
P = 6s
P = 6(2r)
P = 12r
Therefore, the perimeter of the hexagon is 12r.
So, the correct answer is not listed.
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If a regular hexagon circumscribes a circle of radius r, then its perimeter is :a)4√3rb)6√3rc)6rd)12√3rCorrect answer is option 'A'. Can you explain this answer?
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