AB = BC = CD = 4，∠B=60，BE+DF=4

∴△ABC is a regular triangle, BE=CF, ∠ ACF = 60 = ∠ b,

∴AB=AC，

∴△ABE≌△ACF

∴AF=AE,∠BAE=∠CAF

∴∠BAE+∠EAC=∠EAC+∠CAF，

That is, < EAF = < BAC = 60,

∴△AEF is a regular triangle;

② FG⊥BC, extending BC to G,

Then FG= (root number 3)X/2, EC=4-X,

S△CFE= (root number 3)X/2*(4-X)/2= root number 3*X(4-X)/4.

S△AEF=S diamond -S△ Abe -S△AFD-S△CEF?

= S diamond-S△ACD-S△CEF(∵△ABE?△ACF)

=S△ABC-S△CEF

= (root number 3)? x？ /4- (root number 3)X+4 root number 3?