First sketching every part in 2d:
I made the joints and put the kerf in consideration. Some joints' legnthes were minuse the kerf and others were plus the kerf in order to get the spacified legnth.
do the same steps as the side . The legnth of the joints in top edge of the front were plus the kerf and in the other edge were minus the kerf.
do the same steps as the side (but with a dimension 100x100 for the rectangle) then draw a bigger rectangle that contains the shape. The joints' lengthes here were minus the kerf.
Extrude every sketch and join them together.
creat a copy from each component then join them to the box
Save the sketches as DXF then take them to the laser cut machine software and define the cutting process' parameters. The cutting speed was 60m/s. Then downlowad the file to the machine and choose the file in the machine screen then start the process.