Inside a quadrilateral $ABCD$ there exists a point $P$ such that $AP$ is perpendicular to $AD$ and the line $BP$ is perpendicular to $DC$. Besides, $AB = 7$, $AP = 3$, $BP = 6$, $AD = 5 $ and $CD = 10$. Calculate the area of the triangle $ABC$.
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Tags: geometry
Inside a quadrilateral $ABCD$ there exists a point $P$ such that $AP$ is perpendicular to $AD$ and the line $BP$ is perpendicular to $DC$. Besides, $AB = 7$, $AP = 3$, $BP = 6$, $AD = 5 $ and $CD = 10$. Calculate the area of the triangle $ABC$.