Reason:

The four sides of the (1) square are equal, so DE=AF, ∠ A = ∠ D = 90, AB=AD, so △ ABF △ DAE,

So AE=BF.

(2) ∠ AED = ∠ BFA because △ ABF △ DAE; So ∠AOF=∠AFO+∠OAF=∠AED+∠OAF.

= ∠ d = 90, so AE⊥BF.

(3) BE, because AE⊥BF, △AOB and △BOE are right angles △ respectively, and right angles are ∠AOB and ∠BOE respectively.

So AO=√(AB? -Bo? )，OE=√(BE？ -Bo? )=√[(BC？ +CE？ )-Bo? ]=√(BC？ -Bo? +CE？ ); Because AB=BC, OE≥AO, if and only if CE=0, that is, E and C coincide, equal sign, AE and BF are diagonal lines of a square. So AO=OE is not necessarily true, that is, (3) error.

(4)S△AOB=S△ABF-S△AOF, s quadrilateral DEOF=S△ADE-S△AOF, because S△ABF=S△ADE.

So S△AOB=S quadrilateral DEOF.