   Chapter 8.3, Problem 8E 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

For a regular hexagon, the length of the radius is 12 in. Find the length of the radius for the inscribed circle for this hexagon.

To determine

To find:

The length of the radius of inscribed circle in a hexagon.

Explanation

1) Any radius of a regular polygon bisects the angle at the vertex to which it is drawn.

2) Any apothem of a regular polygon bisects the side of the polygon to which it is drawn.

3) The measure of any central angle of a regular polygon of n sides is given by c=360n

4) The radius inscribed circle in a hexagon is equal to the apothem of the hexagon.

Calculation:

Consider a regular hexagon ABCDEF with QE as radius and QG as apothem.

It is given that the length of the radius of the regular hexagon ABCDEF is 12 in. i.e., QD = 12 in.

Use the formula of central angle, c=360n

Substitute n = 6 in c=360n.

c=3606=60

Therefore, EQD=60

With EQD=60 and QE=QD, ΔQED is an equiangular and equilateral triangle

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