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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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For a regular octagon, the length of the apothem is approximately 12 cm and the length of the radius is approximately 13 cm. To the nearest centimeter, find the perimeter of the regular octagon. ________________________

Chapter 7.CT, Problem 14CT, For a regular octagon, the length of the apothem is approximately 12 cm and the length of the radius

To determine

To find:

The perimeter of the regular octagon.

Explanation

Given:

The length of the apothem of the regular octagon = 12 cm.

The length of the radius = 13 cm

Calculation:

To find: the perimeter of the regular octagon.

The perimeter of the octagon is 8 × (length of one side of octagon).

Let us take the triangle, GSO.

We have to find the length of one side of octagon (GF).

Let the length of one side of octagon (GS) = x

GF = GS+SF

GF=x+xGF=2x

By using Pythagorean theorem:

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

This relationship is represented by the formula a2=b2+c2.

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