
If a regular hexagon is inscribed in a circle of radius r, what is its perimeter?
A. 3r
B. 6r
C. 9r
D. 12r
Answer
535.8k+ views
2 likes
- Hint: Given the regular hexagon is inscribed in a circle of radius r. Try to prove that a hexagonal is made of six equilateral triangles by joining the opposite sides of the hexagon.
After that you will observe that the sides of each equilateral triangle is r, equal to the radius of the circle. Now, you can easily find the perimeter of the hexagon.
Complete step-by-step solution -
The regular hexagon is inscribed in a circle of radius r.
So, it is inside the circle.
By joining opposite sides of the hexagon, it forms six (6) central angles at centre O each of which .
And, you see the six triangles are formed.
The two sides of each triangle are the radius of the circle and thus are equal.
The base angles of every triangle are equal.
Since, the central angle is .
This gives,
The triangles are equilateral triangles.
This gives, all sides are equal.
You can observe this in the figure drawn below.
All sides of each triangle are r.
Hence,
Perimeter of regular hexagon
Hence, option B is correct.
Note: This question can be solved easily in this way - (You can do this question by observing and thinking in this way).
A regular hexagon is a polygon whose all sides are equal and it has been made of six equilateral triangles.
Now, if a regular hexagon is inscribed in a circle then its side is equal to the radius of the circle.
Hence, the perimeter of regular hexagon = 6r.
After that you will observe that the sides of each equilateral triangle is r, equal to the radius of the circle. Now, you can easily find the perimeter of the hexagon.
Complete step-by-step solution -
The regular hexagon is inscribed in a circle of radius r.
So, it is inside the circle.
By joining opposite sides of the hexagon, it forms six (6) central angles at centre O each of which
And, you see the six triangles are formed.
The two sides of each triangle are the radius of the circle and thus are equal.
Since, the central angle is
This gives,
This gives, all sides are equal.
You can observe this in the figure drawn below.
Hence,
Perimeter of regular hexagon
Hence, option B is correct.

Note: This question can be solved easily in this way - (You can do this question by observing and thinking in this way).
A regular hexagon is a polygon whose all sides are equal and it has been made of six equilateral triangles.
Now, if a regular hexagon is inscribed in a circle then its side is equal to the radius of the circle.
Hence, the perimeter of regular hexagon = 6r.

Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Chemistry: Engaging Questions & Answers for Success

Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Gautam Buddha was born in the year A581 BC B563 BC class 10 social science CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

What is the median of the first 10 natural numbers class 10 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE
