Metric properties

Let $ABCDEF{A}^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }{E}^{\prime }{F}^{\prime }$ be a regular hexagonal prism with the base edge length of $4\mathrm{cm}$ and the height of $8\mathrm{cm}$. Find the angle between the plane $AB{B}^{\prime }$ and the plane $AE{E}^{\prime }$ (see the picture).

Let $ABCDEF{A}^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }{E}^{\prime }{F}^{\prime }$ be a regular hexagonal prism with the base edge length of $4\mathrm{cm}$ and the height of $4\sqrt{6}\mathrm{cm}$. Find the distance between the lines $FA$ and $C^{\prime }{D}^{\prime }$ (see the picture).

A regular hexagonal prism $ABCDEF{A}^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }{E}^{\prime }{F}^{\prime }$ has the base edge length of $4\mathrm{cm}$ and the height of $6\mathrm{cm}$. Let $S$ be the middle of the top face $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }{E}^{\prime }{F}^{\prime }$. Find the distance between the point $S$ and the line $BC$ (see the picture).

Let $ABCDEF{A}^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }{E}^{\prime }{F}^{\prime }$ be a regular hexagonal prism with the base edge length of $4\mathrm{cm}$ and the height of $8\mathrm{cm}$. Find the distance between the points $E^{\prime }$ and $C$ (see the picture).