Install the Pergo floor tiles until you reach approximately 1 foot away from the hearth area.
Place one of the Pergo tiles up against the hearth pad and draw a pencil line on the hearth all the way across the top of the tile. Slide the tile out of the way and ensure the pencil line on the side of the hearth is dark enough to see easily.
Install a diamond-tipped saw blade into an undercut saw and slide the saw up against the side of the hearth until the blade touches it. Locate the upper depth adjustment knob and raise or lower the saw blade until it lines up with the pencil mark.
Wear protective eyewear and a dust mask and plug in the cord of the undercut saw. Place it at one end of the hearth and turn on the saw. Press the saw against the hearth to cut into it by 1/2 inch. Then, slide the saw slowly and smoothly along the entire length of the hearth to extend the line across
Stop the saw and unplug. Press the saw back up against the side of the hearth and lower the blade until it is flush with the subfloor material. Plug the saw back in and cut all the way across the bottom of the hearth, using the same method as the first cut.
Set the saw aside and place the tip of a chisel in the side of the hearth between the two cut locations. Hit the chisel with a hammer to dislodge the material between the lines. Work your way down along the length of the hearth until you have a 1/2-inch deep groove all the way down the side.
Vacuum the area thoroughly using a shop vac to remove all dust and stone particles before proceeding to install the remaining Pergo.
Continue installing the Pergo from the area where you stopped until you reach the hearth. Then, slide the final row of Pergo under the cut edge of the hearth to hide it. If a full Pergo tile does not fit into the area, cut it to size using a hacksaw or a circular saw.