1. Let the regular hexagon be $A_{1} A_{2} A_{3} A_{4} A_{5} A_{6}$. Points $P_{1}$ and $P_{2}$ are the midpoints of sides $\overline{A_{4} A_{5}}$ and $\overline{A_{3} A_{4}}$. What is the ratio of the areas of triangle $\Delta P_{1} A_{1} P_{2}$ and the regular hexagon $A_{1} A_{2} A_{3} A_{4} A_{5} A_{6}$?