Intermezzo Problem

We have the unit (edge length equal 1)  square and the unit edge equilateral  triangle.

Choose a shape, such that many instances of that shape (maybe flipped or rotated) tile both polygons. There must be no overlaps and no part of the covering shape may lie outside both polygons.

A shape that leaves a smaller percentage of its own area uncovered is a better solution.

Which shape is the best covering solution?