Tiling A Snowflake

There are $84$ triangles in the snowflake so we need $21$ tiles. Each tile covers three blue and one white triangle in the following colouring:

...but there are only $20$ white triangles; so such a tiling is impossible.

Color the area as follows with $42$ gray triangles and $42$ white triangles:

Then there are two types of straight tiles that can be placed on the board - one that covers $1$ white triangle and $3$ gray triangles, and one that covers $3$ white triangles and $1$ gray triangle:

Let $x$ be the number of straight tiles that cover $1$ white triangle and $3$ gray triangles, and let $y$ be the number of straight tiles that cover $3$ white triangles and $1$ gray triangle.

Since each straight tiles covers $4$ triangles, and since there are $84$ triangles, there are $\frac{84}{4} = 21$ total straight tiles, so $x + y = 21$ .

Also, since $42$ gray triangles need to be covered, $3x + y = 42$ .

However, $x + y = 21$ and $3x + y = 42$ leads to $(x, y) = (\frac{21}{2}, \frac{21}{2})$ , a non-integer solution, which is not possible.

Therefore, the tiling is not possible .