Chapter 8.3, Problem 17E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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 pentagon with an apothem of length a = 5.2 cm and each side of length s = 7.5 cm.

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 length of the regular pentagon are 5.2 and 7.5 cm 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 = 7.5 in P = ns.

P = (5)(7.5)

= 37.5 cm

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

Substitute a = 5

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