Metric properties

The rectangular box $ABCDEFGH$ shown in the picture has edges of lengths $|AB|=6\mathrm{cm}$, $|BC|=4\mathrm{cm}$ and $|AE|=8\mathrm{cm}$. Find the distance between the lines $AH$ and $FC$.

The rectangular box $ABCDEFGH$ has edges of lengths $|AB|=6\mathrm{cm}$, $|BC|=4\mathrm{cm}$ and $|AE|=8\mathrm{cm}$. The point $S$ is the center of the left side face $ADHE$ as seen in the picture. Find the distance between the point $F$ and the point $S$.

A regular hexagonal prism $ABCDEF{A}^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }{E}^{\prime }{F}^{\prime }$ has the side $a$ of the length $3\mathrm{cm}$ and the height $v$ of the length $8\mathrm{cm}$. Find the distance between the planes $AE{E}^{\prime }$ and $BD{D}^{\prime }$.

A regular hexagonal prism $ABCDEF{A}^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }{E}^{\prime }{F}^{\prime }$ has the side $a$ of the length $3\mathrm{cm}$ and the height $v$ of the length $8\mathrm{cm}$. Find the angle between the plane $AB{D}^{\prime }$ and the base plane $ABC$. Round the result to two decimal places.