Connecting DE and DF, they divide EFGH into three triangles, and the sum of the areas of EDH, DFG and DEF is the EFGH area.

S△DEF = 1/2EF * EH = 1/2(HD+DG)* EH = S△EHD+S△DFG

So S△DEF= 1/2EFGH.

S△DEF = S□ABCD-S△ADE-S△DFC-S△BEF = 8×8- 1/2×2×8- 1/2×3×8- 1/2×5×6 = 64-8- 12- 15 = 29

The area of ∴EFGH is 2S△DEF=58.