Example 2. For $\triangle A B C=$ with sides $a, b, c$, construct squares outward on each side, with areas sequentially $S_{a}, S_{b}, S_{c}$. If $a+b+c=18$, find the minimum value of $S_{\mathrm{a}}+S_{\mathrm{b}}+S_{\mathrm{c}}$.
Given $(a-b)^{2}+(b-c)^{2}+(c-a)^{2}$ $\geqslant 0$, which means $2\left(a^{2}+b^{2}+c^{2}\right)=2(a b+b c+c a)$. Therefore, $3\left(a^{2}+b^{2}+c^{2}\right) \geqslant a^{2}+b^{2}+c^{2}+2 a b$ $+2 a c+2 b c=(a+b+c)^{2}$. Thus, $S_{1}+S_{v}+S_{r} \geqslant \frac{18^{2}}{3}=108$.

When $a=b=c$, the equality holds, so the minimum value is 108.
This is the method of inequality.