Point in Regular Hexagon

In the diagram, $P$ is a point inside a regular hexagon $ABCDEF$ . The areas of triangles $ABP$ , $CDP$ , and $EFP$ are $\SI{3}{\centi\meter\squared}, \SI{5}{\centi\meter\squared},$ and $\SI{8}{\centi\meter\squared},$ respectively.

Find the area of triangle $BCP$ in $\si{\centi\meter\squared}$ rounded off to the nearest thousandth.

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Source: 平成３０年度　灘中学校・灘高等学校　入試問題　算数　１日目　問題１０

// Nada High School Entrance Examinations 2018, Day 1 of Mathematics, Problem 10