   Chapter 8.3, Problem 26E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# 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 a side of length 12 ft, find the approximate area.

To determine

To find:

The approximate area of a regular dodecagon.

Explanation

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 side is 12 ft.

Substitute s = 12 in s = 8x.

12=8xx=128=1.5ft

Substituting x = 1.5 in a = 15x.

a = 15(1.5)

= 22.5 ft

The total number of sides in a regular dodecagon is 12.

Use the formula for the perimeter of regular polygon, i

### 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

#### Simplify: 3642

Elementary Technical Mathematics

#### Evaluate the expression sin Exercises 116. (2)3

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 3540, rationalize the numerator of each expression. 40. x+3x3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Find f(x) if f(x)=1x2 and f(2) = 0. a) 1x+12 b) 1x12 c) 3x3+38 d) 3x338

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

#### The length of a = 4i – j – 2k is: 11 21

Study Guide for Stewart's Multivariable Calculus, 8th 