tangram tasks

there are several tangram interactives available
e.g. this one (utilising geogebra)

the tangram dissection:

find how to fit all of the 7 tangram pieces into these outlines:

you could consider the perimeters
(there are 4)

[in terms of multiples of the square root of 2 and integers]

an interesting set of 3 shapes that look the same size but are not (a kind of paradox)

find outline shapes that have just one line of symmetry (using all 7 tangram pieces)
some examples (several more can be found):

find an outline shape with rotational symmetry, order 4, using all the tangram pieces
(slightly cheating, with a gap in the centre)
or the square