#### Answer

30 ft

#### Work Step by Step

Lets extend AE , BE, DF ,FC and take DG perpendicular to BC
Now BCFE is a rectangle EF=BC = 13ft
AD = HG = 7ft
than BH = GC = 3ft each
By pythagoras theorem on right triangle ABH
$AB^{2}$ =$BH^{2}$ + $AH^{2}$
$AB^{2}$ = $3^{2}$ + $4^{2}$
$AB^{2}$ = 9 +16 = 25
AB = 5
AB = DC = 5ft
The perimeter of ABCD is
AB + BC + CD + DA = 5 + 13+5 +7 = 30 ft