While this will not directly answer your question, I'd like to offer an alternative solution.

Modify Existing Molding

If it were me. I'd get some transition molding, with a profile like this.

I'd then set up my table saw to rip the piece, to remove the angle profile on the back edge.

Which would give me a profile like this.

Once I had my molding ripped to size, I'd create a border around the hearth using 45° butt joints.

When installing the flooring, I'd stop short of the hearth to compensate for my expansion gap and the thickness of the moldings leg (the piece that hangs down). Once the flooring was installed, I'd install my molding.

The molding allows the floor to expand and contract, while also providing an attractive transition between wood and brick.

_{Note: If you match the molding color to the flooring color, the transition will be less noticeable.}

Manufacturers require expansion around the entire perimeter of your floating floor. Depends on whether or not you want to maintain your warranty. If you don't care, fly at er. You may or may not end up with issues. Depending on the height of the tile, I like to use an Edge Mold which butts up to the tile instead of overlapping it. It still overlaps the laminate, offering a warranty approved solution. Last week I had to deny a warranty claim by a builder who butted all his floating engineered hardwood tight to tile. The flooring started to squeak a couple months after completion. Badly. Sorry "builder". He was out a substantial sum. Your 10x11 room may survive unscathed.