Answer
$4$ 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.
