Chapter 7.CR, Problem 33CR

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

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

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

Given that the radius of the circle is 10 cm

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