3. For a regular hexagon $\mathrm{ABCDEF}$ with side length $\mathrm{a}$, $\mathrm{AP} \perp$ the plane of the hexagon and $\mathrm{AP}=\mathrm{h}$. Find: (1) the distance from point $\mathrm{P}$ to $\mathrm{BC}$; (2) the distance from point $\mathrm{P}$ to $\mathrm{CD}$; (3) the distance from point $\mathrm{P}$ to $\mathrm{DE}$.
$\begin{array}{l}\text { Ans: } \\ \frac{1}{2} \sqrt{3 \mathrm{a}^{2}+4 \mathrm{~h}^{2}} ;(2) \sqrt{3 \mathrm{a}^{2}+\mathrm{h}^{2}} ; \\ \text { (3) } \sqrt{\left.3 \mathrm{a}^{2}+\mathrm{h}^{2}\right)}\end{array}$