## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.2 - The Law of Cosines - Exercise Set - Page 730: 25

#### Answer

The area of a triangle is approximately $4$ square feet.

#### 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. The area of the triangle is given by \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( 4+4+2 \right)=5 \\ \end{align} By substituting the values of s and a, b, c we get, \begin{align} & A=\sqrt{5\left( 5-4 \right)\left( 5-4 \right)\left( 5-2 \right)} \\ & A=\sqrt{15}=3.87 \\ & A\simeq 4 \\ \end{align}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.