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Mathematical geometry Olympics
The shade part in that figure consists of four congruent small square,

The side length of each small square is (2) times that of the big square,

Because the side length of a big square is 40cm. ,

So the side length of the upper square is 10 root 2cm,

So the area of a small square is 200cm^2,

The shaded area is 800cm^2.