Precalculus (6th Edition) Blitzer

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

Chapter 6 - Review Exercises - Page 798: 15


$4$ square meters

Work Step by Step

Heron’s formula to find the area of triangle is given by: $\text{Area}=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$ Where $s=\frac{a+b+c}{2}$ Here, $\begin{align} & s=\frac{2+4+5}{2} \\ & =\frac{11}{2} \end{align}$ So, the area of the triangle will be $\begin{align} & \sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}=\sqrt{\frac{11}{2}\left( \frac{11}{2}-2 \right)\left( \frac{11}{2}-4 \right)\left( \frac{11}{2}-5 \right)} \\ & =\sqrt{\frac{11}{2}\cdot \frac{7}{2}\cdot \frac{3}{2}\cdot \frac{1}{2}} \\ & =\sqrt{\frac{231}{16}} \end{align}$ Using the calculator we get $\sqrt{\frac{231}{16}}\approx 4$ So, the area of the triangle is approximately $4$ square meters.
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