Question 9
Using cardboard equilateral triangles with side $1$, an equilateral triangle with side $2^{2004}$ is formed. From this triangle, the small triangle with side $1$ is extracted, whose center coincides with the center of the larger triangle.
Determine if it is possible to completely cover the remaining surface, without overlaps or gaps, if only pieces in the shape of an isosceles trapezoid are available, each of which is made up of three equilateral triangles with side $1$.
Determine if it is possible to completely cover the remaining surface, without overlaps or gaps, if only pieces in the shape of an isosceles trapezoid are available, each of which is made up of three equilateral triangles with side $1$.