   Chapter 8.3, Problem 30E ### 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
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# 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 measure of each apothem is 4 cm, and each side measures exactly 8 ( 2 − 1 ) cm. Find the exact area of this regular polygon.

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 length of the apothem and side of a regular octagon are respectively 4 and 8(21) cm.

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 = 8(21) in P = ns.

P = (8) 8(21)

= 64(21)<

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