2. Triangle $A B C$ of area 1 is given. Point $A^{\prime}$ lies on the extension of side $B C$ beyond point $C$ with $B C=C A^{\prime}$. Point $B^{\prime}$ lies on extension of side $C A$ beyond $A$ and $C A=A B^{\prime}$. $C^{\prime}$ lies on extension of $A B$ beyond $B$ with $A B=B C^{\prime}$. Find the area of triangle $A^{\prime} B^{\prime} C^{\prime}$.
Solution. Let us prove that each of the triangles $A^{\prime} B^{\prime} C, A^{\prime} B C^{\prime}, A^{\prime} B^{\prime} C^{\prime}$ has area 2 so that the area of large triangle is 7 . Let us look at $A B^{\prime} C^{\prime}$ and draw the line $B B^{\prime}$.
We have
$$
S_{A B C}=S_{A B B^{\prime}}=S_{B B^{\prime} C^{\prime}}
$$
so $S_{A B^{\prime} C^{\prime}}=2$.