Answer
The area of the triangle is 31 square meters.
Work Step by Step
According to the given data, the area of the triangle is calculated by using the Heron’s formula:
$\text{Area}=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$
Here, s is half of the perimeter of the triangle.
For the given triangle, the value of s is calculated by the following formula:
$s=\frac{1}{2}\left( a+b+c \right)$
Therefore,
$\begin{align}
& s=\frac{1}{2}\left( 7+9+12 \right) \\
& s=14
\end{align}$
Thus,
$\begin{align}
& \text{Area}=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)} \\
& =\sqrt{14\left( 14-7 \right)\left( 14-9 \right)\left( 14-12 \right)} \\
& =\sqrt{980} \\
& =31
\end{align}$
Therefore, the required area is 31 square meters.
