so.... notice the picture below
now, we know what the "height" or "altitude" is
now, we also know the perimeter is 18cm
so, k + k + b = 18
or 2k + b = 18
thus \(\bf k=\cfrac{18-b}{2}\)
so... one can say that \(\bf \textit{area of a triangle}=A=\cfrac{1}{2}bh\qquad
\begin{cases}
b=b
\\\\
h=\sqrt{k^2-\left( \frac{b}{2} \right)^2}
\\\\
h=\sqrt{k^2-\frac{b^2}{4}}\\
--------------\\
k=\frac{18-b}{2}\qquad thus\\
--------------\\
h=\sqrt{\left( \frac{18-b}{2} \right)^2-\frac{b^2}{4}}
\end{cases}\\\\
-----------------------------\\\\
A=\cfrac{1}{2}\cdot b\cdot \sqrt{\left( \frac{18-b}{2} \right)^2-\frac{b^2}{4}}\)
and you can simplify it if you wish.. not sure you have to
