   Chapter 8.3, Problem 24E 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 approximate area of a regular pentagon whose apothem measures 6 in. and each of whose sides measures approximately 8.9 in.

To determine

To find:

The area of a regular pentagon.

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 pentagon with apothem a and perimeter P is given by A=12(aP).

Calculation:

It is given that the apothem and side of the regular pentagon are 6 and 8.9 in. respectively.

The total number of sides in a regular pentagon is 5.

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

Substitute n = 5 and s = 8.9 in P = ns.

P = (5)(8.9)

= 44.5 in.

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

Substitute a = 6 and P = 44

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