Assuming the damage extends no farther than that short brown side wall, I would try to replace that entire linear section with a patterned tile design. The one good thing is that the fireplace and the doors are there so it could more easily look like a fireplace hearth that was intentionally extended to include the entryways.

You're welcome; good luck!

I like Elle's idea of a "border" all the way across but maybe something different than the diamond shape tile. Thinking...

How bout slate in an offset pattern? I would use grout color in the dark gray since it's a high traffice area. Like Elle mentioned...two rows, equal width from wall to wall.

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doing a thin border like that will look a bit odd.

get some hex tiles and do something like this, feathering it in w/the wood

You want it to look like it was planned,,,not a cover up. So you may have to cut into the good wood in order to 'randomly' place your tiles.

this will take some precise cutting to get the tiles to fit flush against the wood. you can do it w/a good hand saw or large drummer tool to clean up splinters.

another idea is to do wood hex tiles and stain them the same as your flooring.

or pebble rock

or slate

Kenma, keep in mind that the photo I posted was just an example of the concept and not necessarily the one and only pattern that should be considered. I personally like the idea of a linearly defined geometric area such as a rectangle or a rectangle with a slight further bump out in front of the fireplace. To me the alternative of replacing the uneven damaged area based on the contours of the chosen tile looks a little odd and more like a patch job but, as with most things, it is a matter of personal opinion.