## Precalculus (6th Edition) Blitzer

$4$ square meters
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.