It's all about shearing:Parallelograms LMOA and LKCA have a common base AL and and collinear opposite sides OM and CK. Hence they have the same areas.
Parallelograms LKCA and ACDE have a common base AC and collinear opposite sides LK and DE.
Parallelograms HMOB and HKCB have a common base BH, etc...
Parallelograms HKCB and HKDF have a common base HK, etc...