Chapter 7.3, Problem 13E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Find the lengths of the apothem and the radius of a square whose sides have length 10 in.

To determine

**To find:**

The lengths of the apothem and the radius of a square.

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.

**Calculation:**

Consider a square *ABCD* with *OA* as radius and *OE* as apothem.

It is given that the side of the square ABCD is 10 in. i.e., *AB* = *BC* = *CD* = *DA* = 10 in.

All the angles of a square are of 90Â° i.e.,

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

Therefore,

Now,

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

Therefore, *ED* = *EC*

Now, *DC* = *DE* + *EC*

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