B6. As shown in the figure, $\triangle \mathrm{ABC}$ is divided into six smaller triangles by three lines passing through its three vertices and an interior point. The areas of four of the smaller triangles are marked in the figure. Find the area of $\triangle \mathrm{ABC}$.

 untranslated part:
 


The areas of four of the smaller triangles are marked in the figure, 求 $\triangle \mathrm{ABC}$ 的面积。

Note: The last sentence is a mix of English and Chinese. Here is the fully translated version:

The areas of four of the smaller triangles are marked in the figure. Find the area of $\triangle \mathrm{ABC}$.
If the heights of two triangles are the same, then the ratio of their areas is equal to the ratio of their corresponding base lengths. Therefore, from the figure, we get
$$
\frac{40}{30}=\frac{40+y+84}{30+35+x}, \quad \frac{35}{x}=\frac{35+30+40}{x+84+y},
$$
$\frac{84}{y}=\frac{84+x+35}{y+40+30}$. Solving the first two equations yields $\mathbf{x}=70, \mathrm{y}=56$, which also satisfies the third equation. The area of $\triangle \mathrm{ABC}$ is $30+35+70+84+56+40=315$.