The four pieces of this hinged dissection have plastic on both sides and a wooden core. They can be arranged as an equilateral triangle or a square.The pieces on one side have smaller plastic parts on them so that the equilateral triangle appears to have an inscribed rectangle.
This is a special case of Wheeler's model 4K (trapezoid into a triangle) in his list of decompositions of polygons.
Compare MA.304723.813.
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