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Mathematical geometry problems in primary schools
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.