As shown in the figure, connect DI, EH, GF,

Obviously, the area of △EHI is equal to △DHI, and △DIF is equal to △GIF (the same height as the bottom).

So HBIF+AEIH+IFCG = 2 △ HIF+2 △ EHI+2 △ GIF = 2 △ HIF+2 △ DHI+2 △ DIF = 2 △ DHF = 24.

In terms of proportional relationship, HBIF=4, AEIH=8, IFCG= 12.

Because HBIF:AEHI= 1:2, EI:IH= 1:2.

So IFCG:DEIG= 1:2, so DEIG=24,

So ABCD=4+8+ 12+24=48 (square decimeter)