   Chapter 8.3, Problem 28E 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 octagon, the approximate ratio of the length of an apothem to the length of a side is 6:5. For a regular octagon with a side of length 15 ft, find the approximate area.

To determine

To find:

The approximate area of a regular octagon.

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 octagon 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 6:5.

By proportionality constant, a = 6x and s = 5x.

It is also given that the length of the side is 15 ft.

Substitute s = 15 in s = 5x.

15=5xx=155=3ft

Substituting x = 3 in a = 6x.

a = 6(3)

= 18 ft

The total number of sides in a regular octagon is 8.

Use the formula for the perimeter of regular polygon, i.e., perimeter = ns

Substitute n = 8 and s = 15 in P = ns

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