Total width/length/depth of the object

How can I get that kind of measurement? (left picture)

look in the N panel
subpanel for dimensions

note: might need to control-A you object to get right values

happy bl

Please be specific
Do you just want to know the measurement or how to display it ?
For values see the object dimensions, for the display use the Ruler/Protractor tool in the toolshelf under Grease Pencil tab
Do you mean the measurements in the 3d view or in the toolshelf in the 3D Printing tools ?

I think I have found partial solution, this is

Although perfect solution would be like on picture I posted in first post. I am aware this is ruler tool, but it relies on snapping on vertexes, so it’s hard to get bounding box alike measure with it.