Because the curve | xy |+ 1 = | x |+| y | can be transformed into

(|x|- 1)(|y|- 1)=0, that is |x|= 1 or |y|= 1.

The graph of the known equation is four straight lines X = 1, X =- 1, Y = 1, y =-1;

So the figure it surrounds is a square with a side length of 2.

Therefore, the area surrounded by the graph represented by the formula | xy |+ 1 = | x |+| y | is

2*2=4