依题意，得
S_{六边形ABCDEF}=S_□MNRQ-S_△ABM-S_△BCN-S_△CDR-S_△DEF-S_△AFQ，
=6×6-

1

2

×2×4-

1

2

×2×2-

1

2

×4×2-

1

2

×3×1-

1

2

×1×4，
=22.5平方厘米．