[mkxmvdmc] Square pieces with large bounding box

Cut a square into 4 rectangles by 2 orthogonal cuts.  Rearrange the rectangles into a new shape with all 4 meeting at a vertex.  Consider the bounding box around the new shape.  Over all cuts and rearrangements, which has the largest bounding box?

Repeat with a cube.  Repeat with only the subset of arrangements possible for a 2x2 mirror cube.