   Chapter 7.3, Problem 12E 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

If the apothem of a square measures 5 cm, find the perimeter of the square.

To determine

To find:

The perimeter of the 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.

3) The perimeter of a regular polygon is given by ns, where n is the number of sides and s is the length of any side.

Calculation:

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

It is given that the length of apothem is 5 cm i.e., OE = 5cm.

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

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