(2005? Suqian) as shown in the figure, there is a square plastic template ABCD with a side length of 4, and the right-angled vertex of a large enough right-angled triangular plate falls at point A,

∴∠D=∠ABC=90，AD=AB，

∴∠ABE=∠D=90，

∫∠EAF = 90，

∴∠DAF+∠BAF=90，∠BAE+∠BAF=90，

∴∠DAF=∠BAE，

At △AEB and △AFD,

∠∠EAB =∠Dafa = AB∠ Abbe =∠ D,

∴△AEB≌△AFD(ASA)，

∴S△AEB=S△AFD，

∴ They all added the area of quadrilateral ABCF,

We can get the area of quadrilateral AECF = the area of square = 16.

So the answer is: 16.