Cool Puzzle! I had never seen these before.
The tile must extend out. It cannot connect to the next shaded cell because it would be size 6. It cannot block off the unshaded cells, so it must therefor be the F tile.
This is the only cell that is not a border and has no adjacent unshaded cells. It must be the X tile
Through extension and allowing the unshaded to attach, the top left is forced to U tile
L tile is forced through extension and connection
N tile is forced through extension and connection
This is the only location that the I tile fits.
All possibilities for tiles that fit in this location other than P were already used.
With P used, that leaves only T for the bottom left corner.
Through extension and connection, only Z fits in the bottom middle
Through extension and connection, W is the only tile that fits on the left.
The unshaded cell to the right and up blocked the V tile, so the Y tile is the only one that fits
There are two possible orientations for the V tile. One blocks off half of the puzzle and prevents connection, therefore only one orientation remains to solve the puzzle.