Let $P$ the intersection point of the diagonals of a convex quadrilateral $ABCD$. It is known that the area of triangles $ABC$, $BCD$ and $DAP$ is equal to $8 cm^2$, $9 cm^2$ and $10 cm^2$. Find the area of the quadrilateral $ABCD$.
Problem
Source: V.A. Yasinsky Geometry Olympiad 2018 X-XI p2 [Ukraine]
Tags: geometry, area of a triangle, areas