5. On the sides $A B$ and $B C$ outside the triangle $A B C$, two equilateral triangles $A B M$ and $B C N$ are constructed. Points $P, Q$, and $R$ are the midpoints of segments $A B, M N$, and $B C$ respectively. Find the area of triangle $P Q R$, if the length of side $A C$ of triangle $A B C$ is 1.
Answer: $\quad S_{P Q R}=\frac{\sqrt{3}}{16}$.

Grading Criteria, 10th Grade

## Preliminary Round of the ROSATOM Industry Physics and Mathematics Olympiad for Schoolchildren, Mathematics

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