Question 3
We say that an equilateral triangle on the plane is in *standard position* if one of its sides is horizontal and the opposite vertex lies above that side. We have $n$ equilateral triangles $S_1, S_2, \dots, S_n$, all of which are in standard position. For each triangle $S_i$, denote by $T_i$ its medial triangle. Let $S$ be the region of the plane covered by the triangles $S_1, S_2, \dots, S_n$, and let $T$ be the region of the plane covered by the triangles $T_1, T_2, \dots, T_n$. Prove that $\text{area}(S) \le 4 \cdot \text{area}(T)$.