Square & Equilateral Triangle

I have never been a huge fan of shape forming puzzles. But after I played with Emrehan Halici's Four Triangles Five Shapes, and more recently Andrea Rover's Growing Triangle, this sort of puzzles, plus the "form-a-symmetrical shape" ones have gotten more of my attention (and liking). I have also recently designed something along similar lines and hopefully will be able to showcase it at IPP37 this coming August.

Square & Equilateral Triangle (SET) is Halici's IPP36 Exchange Puzzle. There are two goals here; use the five irregular shaped pieces to form a square and the same five pieces to form an equilateral triangle (a triangle with three sides of equal length).

It makes me wonder about the genius of Turkish Halici to be able to come up with a design for two different (and symmetrical) shapes using the same pieces; incredible! Unlike his Four Triangles Five Shapes which I failed dismally, I am proud to say that I managed to solve SET without any help, although it took me a number of short puzzling sessions over several days.

I managed to solve the square within a matter of minutes, but the equilateral triangle took about fifteen times longer...it simply eluded me despite my many attempts to try the different combination of putting the five pieces side by side. Finally the A-ha moment arrived one day during a lunch time break.

[Edit 20 April 2017 - Stanislav Knot has come up with an additional 9 different shapes using the 5 pieces. Thanks Stan!]

For folks who are into this sort of puzzles, the SET has just the "right level of difficulty" for an exchange puzzle; one relatively easy goal to get the juices going and a second much tougher challenge. Anyone keen to see the two solutions please PM me here.