   Chapter 7.CR, Problem 29CR 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 a regular polygon, the apothem measures 3 in. Each side of the same regular polygon measures 6 in.a) Find the perimeter of the regular polygon.b) Find the length of radius for this polygon.

To determine

a)

To find:

The perimeter of the regular polygon.

Explanation

Given:

In a regular polygon, the apothem measures 3 inch and each side of the same regular polygon measures 6 inch.

Postulate used:

Angle-addition postulate: (Generalized form)

The measure of an angle equals the sum of the measures of its parts.

The measure of central angle of a regular n-sided polygon is C=360n.

Calculation:

To find the perimeter we need to know the number of sides in the regular polygon.

Whatever number of sides the regular polygon has, there will be an isosceles formed by radii of the polygon and the apothem of the polygon acts as the altitude of the triangle.

The triangle with altitude (apothem) in a regular polygon is shown below

Since the two triangles formed by the altitude are isosceles right triangles, the base angles will be 45.

By angle-addition postulate, the central angle is 90

To determine

b)

To find:

The length of the radius of the polygon.

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