   Chapter 8.3, Problem 27E 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

In Exercises 17 to 30, use the formula A = 1 2 a P to find the area of the regular polygon described.In a regular dodecagon (12 sides), the approximate ratio of the length of an apothem to the length of a side is 15:8. For a regular dodecagon with an apothem of length 12 ft, find the approximate area.

To determine

To find:

The approximate area of a regular dodecagon.

Explanation

Concept:

1) The perimeter of a regular polygon is given by P = ns, where n is the number of sides and s is the length of any side.

2) The area of a regular dodecagon with apothem a and perimeter P is given by A=12(aP).

Calculation:

It is given that the approximate ratio of the length of an apothem to the length of a side is 15:8.

By proportionality constant, a = 15x and s = 8x.

It is also given that the length of the apothem is 12 ft.

Substitute a = 12 in a = 15x.

12=15xx=1215=0.8ft

Substituting x = 0.8 in s = 8x.

s = 8(0.8)

= 6.4 ft

The total number of sides in a regular dodecagon is 12

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Convert the expressions in Exercises 8596 radical form. (x1/2y1/3)1/5

Finite Mathematics and Applied Calculus (MindTap Course List)

Solve Exercise 55 when |CD| = 2 cm.

Single Variable Calculus: Early Transcendentals, Volume I

In Problems 1-4, find the derivative and simplify. 3.

Mathematical Applications for the Management, Life, and Social Sciences

True or False: converges mean exists.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

In how many ways can four compact discs be selected from six different compact discs?

Finite Mathematics for the Managerial, Life, and Social Sciences 