Can this be automated: Selecting multiple seperate rectangle shapes and calculating the L & W

Okay, I have included a script below that should give you what you want. I have also included the screen recording of it working and a copy of your sample file after running the script.

First please note that you have the die paths inside of a group by themselves and the inside of a larger group that includes some "TEST" text. You mentioned above that you would select the die paths before running the script so that is how I set it up... But, since the die paths are in separate groups I selected one die path using the Direct Selection Tool, then used the menu command Select > Same > Stroke Color to get all of the die paths. You can see the process in the screen recording. If all of your files are organized and grouped this way, the script should work just fine, if not, some adjustments will need to be made, as the script only works on the first pathItem in each selected die group.

Once you have your selection, just run the script below and a text frame with the die size info will be placed at the top left of each die path. All text is placed on a separate "non-printable" layer, so you can keep or discard however you please. You can also rerun the script and it will remove any previous/old information before recalculating.

Let me know if you have any questions. Cheers!

(function () {
  // setup variables
  var doc, infoLayer, die, w, h, info, frame;

  // no need to continue if there is no active document
  if (!app.documents.length) {
    alert("No active document.");
    return;
  }

  doc = app.activeDocument;

  // no need to continue if there is no active selection
  if (!doc.selection.length) {
    alert("No active selection.");
    return;
  }

  // cleanup old info if found
  try {
    infoLayer = doc.layers.getByName("DIE INFORMATION");
    infoLayer.remove();
  } catch (error) {
    $.writeln("infoLayer not present");
  }

  // create a "non-printing" layer to hold the die information
  infoLayer = doc.layers.add();
  infoLayer.name = "DIE INFORMATION";
  infoLayer.printable = false;

  // please note: in the sample file, each die was grouped by iteself and
  // withing another larger group that included a few text boxes so this script
  // only acts on the first pathItem within the die pathItem group

  // iterate over each selected object
  for (var i = 0; i < doc.selection.length; i++) {
    die = doc.selection[i].pathItems[0];
    w = UnitValue(die.width, "px");
    h = UnitValue(die.height, "px");
    // format the info as:
    // XX.XXXX in x XX.XXXX in
    // XX.XXXX sq/in
    info =
      w.as("in").toFixed(4) +
      " in x " +
      h.as("in").toFixed(4) +
      " in\n" +
      (w.as("in") * h.as("in")).toFixed(4) +
      " sq/in";
    // add a new text frame at the top left of the die with the die info
    frame = infoLayer.textFrames.add();
    frame.position = Array(die.left, die.top);
    frame.textRange.size = 12;
    frame.contents = info;
  }
})();