A frictionless pivot at its midpoint $P$ holds a uniform rectangular board. Two forces act within the plane of the board. Force $F$ is applied at corner $Q$, while force $2.5F$ is applied at corner $R$. The perpendicular distance from the line of action of force $F$ to point $P$ is $20\,\text{cm}$. The board remains in equilibrium. What is the area of the board?
- A$160\,\text{cm}^2$
- B$320\,\text{cm}^2$
- C$640\,\text{cm}^2$
- D$1600\,\text{cm}^2$