Draw an equilateral triangle. Divide it into four identical shapes. Remove the bottom left-hand shape. Now divide the resulting shape into four identical shapes.
(In reply to
re: I can do this! (spoiler) by Jer)
Thanks, Jer! Since the trapezoid with three equal sides and one unequal is unnamed, I propose a "perplexoid". Further, if the 4th side is smaller I prefer "acute perplexoid" and if it is larger "obtuse perplexoid". The triamond, then, is an "obtuse perplexoid", where the large side is exactly twice the size of any other side.
re(2): I can do this! (spoiler)
