   Chapter 7.3, Problem 13E 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

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 90° i.e., A=B=C=D=90.

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

Therefore, ODE=45

Now, ΔODE is a 45°-45°-90° triangle.

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

Therefore, ED = EC

Now, DC = DE + EC

10=DE+DE10=2DEDE=5in

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