Chapter 7.3, Problem 14E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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Find the lengths of the apothem and the radius of a regular hexagon whose sides have length 6 cm.

To determine

**To find:**

The lengths of the apothem and the radius of a regular hexagon.

Explanation

**Approach:**

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

**Calculation:**

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

It is given that the side of the regular hexagon *ABCDEF* is 6 cm i.e., *AB* = *BC* = *CD* = *DE* = *EF* = *FA* = 6 cm

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

Therefore, *GE*= *GD*

Now, *DF* = *GE* + *GD*

The regular hexagon has 6 sides.

Use the formula of central angle,

Substitute *n* = 6 in

Therefore,

With

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