Hard tangrams look friendly and are not. The outlines are chunky, with few spikes or tails to tell you where a piece must go, and there is no internal line to lean on. Each board can only be filled a handful of ways, so most places a large triangle will fit turn out to be dead ends, and you find out five pieces later.
Expect to take pieces back out. Solve the fussiest corner you can find, keep the square and parallelogram for last, and when a board stalls, move a large triangle before anything else. If you are new to the game, warm up on the daily puzzle, which rotates through every difficulty across the week.