   Chapter 8.3, Problem 29E 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 polygon of 12 sides, the measure of each side is 2 in., and the measure of an apothem is exactly ( 2 + 3 )   in . Find the exact area of this regular polygon.

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 length of the side and apothem of a regular polygon are respectively 2 and (2+3)in.

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

Substitute n = 12 and s = 2 in P = ns

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