We say that two triangles $T_1$ and $T_2$ are contained one in each other, and we write $T_1 \subset T_2$, if and only if all the points of the triangle $T_1$ lie on the sides or in the interior of the triangle $T_2$. Let $\Delta$ be a triangle of area $S$, and let $\Delta_1 \subset \Delta$ be the largest equilateral triangle with this property, and let $\Delta \subset \Delta_2$ be the smallest equilateral triangle with this property (in terms of areas). Let $S_1, S_2$ be the areas of $\Delta_1, \Delta_2$ respectively. Prove that $S_1S_2 = S^2$. Bonus question: : Does this statement hold for quadrilaterals (and squares)?