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)
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.