Chapter 11.CR, Problem 25CR

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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*In Exercises 21 to 30, use the drawings, where provided, to solve each problem, Angle measures should be found to the nearest degree; lengths should be found to the nearest tenth of a unit.*

The apothem length of a regular pentagon is approximately 3.44 cm. What is the approximate length of each side of the pentagon?

To determine

**To find:**

The approximate length of each side of the regular pentagon which has its apothem length as 3.44 cm.

Explanation

**Procedure used:**

In any right triangle ABC with

**Calculation:**

**Given:**

The length of the apothem of a regular pentagon

Let ABCDE be the pentagon with centre ‘o’.

Consider the radii OA and OE of the pentagon adjacent to the apothem OF.

Now, calculate the angle subtended between the radii.

Central angle of the pentagon

Thus,

The apothem bisects the central angle of the pentagon.

Thus,

Now, consider the right triangle EOF, in which

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