Chapter 8.3, Problem 27E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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=15xâ‡’x=1215=0.8â€‰ft

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

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