Example 2. As shown in the figure,
$2, P$ is a point inside the triangle,
where the areas of the four
small triangles are marked in the figure. Find the area of $A B C$. (Third A1ME)

Note: The translation keeps the original text's line breaks and format as requested. However, the mathematical notation and the figure reference (like "As shown in the figure") are kept in their original form, as they are standard across languages. If the figure is not actually present, the reference to it might need to be adjusted.
Solve $-\frac{S \triangle \triangle P D}{S \triangle C D}=\frac{B D}{C D}$,
X
$\frac{S \therefore \operatorname{LA} 1}{S \triangle \mathrm{CAD}}=\frac{B D}{C D}$.
Let $S \triangle \mathrm{BPF}=x, S: A P E=y$,

Then
$$
\begin{array}{l}
S \frac{\mathrm{BAD}}{S-\mathrm{CAD}}=-\frac{S P C D}{S \triangle \mathrm{CPD}}=\frac{B D}{D C}, \\
\frac{84+x+40}{y+35+30}=\frac{40}{30} . \\
\frac{S-C B D}{S-A B R}=\frac{S \triangle C P R}{S}=\frac{C E}{E A}, \\
\frac{40+30+35}{x+84+y}=\frac{35}{y} .
\end{array}
$$

Solve the system of equations $\frac{84+x+40}{y+35+30}=\frac{40}{30}$,
$$
\frac{40+30+35}{x+84+y}=\frac{35}{y}
$$

Get $\left\{\begin{array}{l}x=70, \\ y=56 .\end{array}\right.$
Therefore, $S \triangle \triangle B C=315$.