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MathNet 2022-part-03 — 197 problems (EN–VI) Question 186

Math Olympiad Vault · MathNet 2022-part-03 — 197 problems (EN–VI)

Question 186

Consider the equilateral triangle $PQR$. Inside this triangle the regular hexagon $ABCDEF$ is drawn. Points $B$, $D$ and $F$ are the midpoints of the sides of the triangle $PQR$. The area of the pentagon $QBAFR$ is equal to $1$.
Question illustration
What is the area of the triangle $PQR$?
A) $\frac{11}{10}$
B) $\frac{7}{6}$
C) $\frac{6}{5}$
D) $\frac{5}{4}$
E) $\frac{4}{3}$