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The last question in the junior high school graduation exam mathematics examination paper
The method is a bit troublesome, but it is also 3/8.

Let the coordinate of a after moving be (a-a+3).

Calculate the overlapping area S=-a (square) /2+3a/2-3/4.

When a moves, the coordinates are (3/2? 3/8) Maximum area: 3/8.

(I can't see the picture clearly, sorry, it was taken by the computer)