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See diagram.

The two parallel sides of U will have the center of mass at the center of the rectangle formed by the verticles. It is at E (L/2 , L) if you take the origin at lower left corner.  If origin is taken as the center of the middle side (2L), then it is at E (L/2,0).

Now the center of mass of side 2L and E will be at the center in between, as they have equal masses and lengths 2L.

Center of mass is at F ( L/4,  L) if the origin is at lower left corner.  It is at F (L/4, 0) if the origin is at the center of side 2L.

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