   Chapter 8.CT, Problem 7CT 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

Use Heron’s Formula to find the exact area of a triangle that has lengths of sides 4 cm, 13 cm, and 15 cm.

To determine

To find:

The exact area of the triangle using Heron’s formula.

Explanation

Given:

A triangle that has lengths of sides 4 cm, 13 cm, and 15 cm.

Theorem:

If the three sides of a triangle have lengths a, b, and c, then the area A of a triangle is given by A=s(s-a)(s-b)(s-c) where the semi-perimeter of the triangle is

s=12(a+b+c) which is called the Heron’s formula.

Calculation:

From the given, let a=4 cm., b=13 cm., and c=15 cm.

Calculating s by s=12(a+b+c).

s=124+13+15

s=1232

s=16 cm

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