There are 4 different hexagons you can make with tangrams. 2 of them are:
1) Put the two large triangles together to form a square, then put the two smallest triangles together to form a square, as well. Line up the small square along one side of the big square. Next, use the actual one-piece square and put it next to the smallest triangle-made square. Now put one of the short sides of the parallelogram on whichever one of the small squares you please so that the middle-sized triangle may have its hypotenuse against the big square and one of its legs against the parallelogram.
2) Use the biggest triangles to make one huge triangle. Separately, put the square between the two little triangles so that they make a trapezoid. Now you can connect the hypotenuse of one of the big triangles with the longest side of the trapezoid. Put the the short side of the parallelogram along the bottom of the opposite big triangle's hypotenuse, then put the middle-sized triangle in between the parallelogram with the rest of the hypotenuse.
1) Put the two large triangles together to form a square, then put the two smallest triangles together to form a square, as well. Line up the small square along one side of the big square. Next, use the actual one-piece square and put it next to the smallest triangle-made square. Now put one of the short sides of the parallelogram on whichever one of the small squares you please so that the middle-sized triangle may have its hypotenuse against the big square and one of its legs against the parallelogram.
2) Use the biggest triangles to make one huge triangle. Separately, put the square between the two little triangles so that they make a trapezoid. Now you can connect the hypotenuse of one of the big triangles with the longest side of the trapezoid. Put the the short side of the parallelogram along the bottom of the opposite big triangle's hypotenuse, then put the middle-sized triangle in between the parallelogram with the rest of the hypotenuse.