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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

The length of the radius of a circle inscribed in a regular hexagon is 10 cm. Find the perimeter of the hexagon.

To determine

To find:

The perimeter of the hexagon.

Explanation

Given:

The length of the radius of a circle inscribed in a regular hexagon is 10 cm.

Calculation:

Consider a circle of radius 10 cm inscribed in a regular hexagon.

Draw six lines from the center to the circle to the vertices of the hexagon, dividing the hexagon into six equilateral triangles.

Consider an equilateral triangle.

The radius of the circle equals the height of the equilateral triangles of side s as shown in the figure.

We know the altitude of the equilateral triangle divides the triangle into two right triangles.

Thus by Pythagoras theorem, we get s2=R2+(s2)2

s2=R2+(s2)2R2=s2s24R2=34s2R=32s

Given that the radius of the circle is 10 cm

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