5.2.4.43 Various Problems on the Plane

Condition: a convex quadrangle is given \ (a b c d \). Direct \ (a d \) and \ (b c \) intersect at point \ (n, \ mathrm {a} \) straight \ (c d \) and \ (a b \) at the point \ (m \). The ratio of segments \ (c d \) and \ (c m \) is equal to \ (22: 3 \), the area of the triangle \ (a b n \) is \ (2 /11 \), and the area of the triangle \ (b m n-3 /11 \). Find the area of the triangle \ (a c d \).