4.15. a) The diagonals of a convex quadrilateral $ABCD$ intersect at point $P$. The areas of triangles $ABP$, $BCP$, $CDP$ are known. Find the area of triangle $ADP$.

b) A convex quadrilateral is divided by its diagonals into four triangles, the areas of which are expressed as integers. Prove that the product of these numbers is a perfect square.
4.15. a) Since $S_{A D P}: S_{A B P}=D P: B P=S_{C D P}: S_{B C P}$, then $S_{A D P}=$ $=S_{A B P} \cdot S_{C D P} / S_{B C P}$.

b) According to problem a) $S_{A D P} \cdot S_{C B P}=S_{A B P} \cdot S_{C D P}$. Therefore

$$
S_{A B P} \cdot S_{C B P} \cdot S_{C D P} \cdot S_{A D P}=\left(S_{A D P} \cdot S_{C B P}\right)^{2}
$$