   Chapter 7.3, Problem 36E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Is there a regular polygon with 12 diagonals? If so, how many sides does it have?

To determine

To find:

The number of sides of a regular polygon if it exists.

Explanation

Approach:

The number of diagonals of a regular polygon of n sides is given by D=n(n3)2

Calculation:

It is given the regular polygon has 12 diagonals.

Use the formula for the number of diagonals of a regular polygon, D=n(n3)2

Substitute D = 12 in D=n(n3)2

12=n(n3)2n(n3)=24n23n=24n23n24=0

Use the quadratic formula to find the possible value of n

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