An equilateral triangle of side length 3 can be covered by three trapeziums (Fig. 4). All equilateral triangles with side length being divisible by 3 can be partitioned into equilateral triangles of side length 3. Hence all equilateral triangles with side length being divisible by 3 can be covered by trapeziums of given shape.

Fig. 4

On the other hand, whenever one partitions an equilateral triangle of side length $n$ into equilateral triangles of side length 1, the number of the small triangles is $n^2$ since multiplying the side length by $n$ causes the area to increase $n^2$ times. Consequently, the desired covering is possible only if the number $n^2$ is divisible by 3. The latter condition implies that $n$ must be divisible by 3 since 3 is prime.