   Chapter 8.CR, Problem 25CR 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

The length of the radius of a circle inscribed in an equilateral triangle is 7 in. Find the area of the triangle.

To determine

To find:

The area of the triangle.

Explanation

Formula:

The area of an equilateral triangle (all sides congruent) can be found using the formula

A=34s2

Where s is the length of one side of the triangle.

Calculation:

Suppose a circle is inscribed in equilateral triangle. The radius of the circle is 7 in.

Sketch the circle in equilateral triangle:

The radius is the short side of a 30-60-90 triangle containing half of the base of the triangle and the apothem. Thus, we obtain:

a = 7

Half of the base of the triangle = a3=73

Since this is half of a side, we see that a whole side is

s=2(73)=143 in

To find the area of an equilateral triangle:

A=34s2

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