IKMC 2027 - Grades 7-8 - Self-study SET 2 - Thematic Batch 3 Question 20

Points $M$ and $N$ lie on sides $AD$ and $DC$ of square $ABCD$. Segments $BN,BM,AN,CM$ divide it into eight regions of areas $S_1,S_2,\ldots,S_8$ as shown. Which sum below equals $S_8$?