Given,
$r_1=36, r_2=18$ and $r_3=12$
We know that, in a $\triangle A B C$
$\frac{1}{r}=\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}$
$\Rightarrow \frac{1}{r}=\frac{1}{36}+\frac{1}{18}+\frac{1}{12} \Rightarrow \frac{1}{r}=\frac{2+4+6}{72}$
$r=6$
Now, we know that,
$\begin{aligned} & \Delta^2=r \cdot r_1 \cdot r_2 \cdot r_3=6 \times 36 \times 18 \times 12 \\ & \Delta^2=6^2 \times 6^2 \times 6^2\end{aligned}$
$\Delta=6 \times 6 \times 6=216$
Again we know that,
$r=\frac{\Delta}{S}=\frac{216}{S}$
$\Rightarrow \quad S=\frac{216}{6}=36$