Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 7 - Section 7.3 - More about Regular Polygons - Exercises - Page 333: 34

Answer

There is no regular polygon with 12 diagonals.

Work Step by Step

If $n$ is the number of vertices of a regular polygon, the number of diagonals is: $\frac{n(n-3)}{2}$ If a regular polygon has 6 vertices, the number of diagonals is: $\frac{n(n-3)}{2} = \frac{6(6-3)}{2} = 9$ If a regular polygon has 7 vertices, the number of diagonals is: $\frac{n(n-3)}{2} = \frac{7(7-3)}{2} = 14$ If the number of vertices is less than 6, the number of diagonals is less than 9. If the number of vertices is more than 7, the number of diagonals is more than 14. Therefore, there is no regular polygon with 12 diagonals.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.