   Chapter 8.3, Problem 20E 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.Find the area of a regular octagon with an apothem of length a = 7.9 ft and each side of length s = 6.5 ft.

To determine

To find:

The 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 apothem and length of the regular octagon are 7.9 and 6.5 ft respectively.

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 = 6.5 ft in P = ns.

P = (8)(6.5)

= 52 ft

Use the formula of area of regular octagon, A=12(aP)

Substitute a = 7

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