$[$ The ratio of the areas of triangles with a common base or common height $]$

On side $A C$ of triangle $A B C$, a point $A_{1}$ is taken, and on the extension of side $B C$ beyond point $C$, a point $C_{1}$ is taken, the length of segment $A_{1} C$ is $85 \%$ of the length of side $A C$, and the length of segment $B C_{1}$ is $120 \%$ of the length of side $B C$. What percentage of the area of triangle $A B C$ is the area of triangle $A_{1} B C_{1}$?
$S_{A_{1} B C_{1}}=1,2 S_{A_{1} B C}=(1,2 \cdot 0,85) \cdot S_{A B C}=1,02 S_{A B C}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_67482594d9a3488694ecg-34.jpg?height=366&width=744&top_left_y=1278&top_left_x=657)

Answer

$102 \%$.