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?