KöMaL 2025 C1849

Let $N_1$, $N_2$ and $N_3$ be the quadrisection points on side $AB$ of convex quadrilateral $ABCD$ going from $A$ to $B$. Let $M_1$, $M_2$ and $M_3$ be the quadrisection points on side $DC$ going from $D$ to $C$. Point $N_4$ is obtained by extending side $AB$ beyond point $B$ with the quarter of the length of side $AB$. Similarly, point $M_4$ is obtained by extending side $DC$ beyond point $C$ with the quarter of the length of side $DC$. Determine the area of quadrilateral $ABCD$ if it's given that the area of quadrilateral $AN_1M_1D$ is $8$ units and the area of quadrilateral $BN_4M_4C$ is $10$ units.