Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.2 - The Law of Cosines - Exercise Set - Page 730: 27


The area of a triangle is approximately $22$ square meters.

Work Step by Step

The area of a triangle is calculated using Heron's formula where $s$ is equal to half the perimeter of the triangle. Area of the triangle $\begin{align} & A=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)} \\ & \\ \end{align}$ where $\begin{align} & s=\frac{1}{2}\left( a+b+c \right) \\ & s=\frac{1}{2}\left( 14+12+4 \right)=15 \\ \end{align}$ By substituting the values of s and a, b, c we get, $\begin{align} & A=\sqrt{15\left( 15-14 \right)\left( 15-12 \right)\left( 15-4 \right)} \\ & A=\sqrt{495}\simeq 22 \\ \end{align}$
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