CEMC Hypatia, 2005

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

In the diagram, $\triangle ABC$ is equilateral with side length $4$ . Points $P$ , $Q$ and $R$ are chosen on sides $AB$ , $BC$ and $CA$ , respectively, such that $AP = BQ = CR = 1$ .
(a) Determine the exact area of $\triangle ABC$ . Explain how you got your answer.
(b) Determine the exact areas of $\triangle PBQ$ and $\triangle PQR$ . Explain how you got your answers.

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