I have a cantor set$\displaystyle F$ in (0,1) and its hausdorff dimension is $\displaystyle dim_H (F)= \frac{1}{7}$ I have managed to show that $\displaystyle dim_H (F \times [0,1])=\frac{8}{7}$.

I am trying to determind $\displaystyle dim_H (E)$ where $\displaystyle E = ( F \times \Re) \bigcup (\Re\times F)$

I have no clue how to do this or what $\displaystyle E = ( F \times \Re) \bigcup (\Re \times F)$ actually means in terms of fractals.

Any help or explanations will be really appreciated.