How many ways can you make a square with the tangram pieces?

Answer 1

Answer
only in 3 or 8n ways

Another answer
Apart from rotating the squares, and also assuming you have double sided pieces, there are two 'ways.'

1.

• (i) Use the two largest triangles to form the upper left half of the square, forming the top, the left side and the diagonal line from top right to bottom left.
  
• (ii) Use the next largest triangle to form the bottom right corner.
• (iii) Place the parallelogram so that the upper right side is filled.
• (iv) Use the remaining pieces in the order: 'triangle, square, triangle' to fill the remaining space.

2.

• As above for steps (i) and (ii)
• (iii) place the parallelogram to fill the bottom left side. You'll need to flip it over to do this.
  
• (iv) Use the remaining pieces in the order: 'triangle, square, triangle' to fill the remaining space.

Of course, pieces can be flipped or rotated, or identically shaped pieces can be swapped. But doing any of these things doesn't fundamentally change the way the square is formed.