prostornina (volumen)
$$ V = \frac{1}{3} O \cdot v $$
površina
$$ P = O + pl $$
ploščina osnovne ploskve
$$
\begin{aligned}
&O = \frac{1}{4} n a^2 \cot\frac{180^\circ}{n} \\ \\
& n = 3 \ \Rightarrow \ O = \frac{\sqrt{3}}{4} a^2 \\ \\
& n = 4 \ \Rightarrow \ O = a^2
\end{aligned}
$$
ploščina plašča
$$ pl = \frac{n a v_a}{2} $$
stranski rob
$$
\begin{aligned}
s &= \frac{v}{\sin\alpha_1} \\ \\
s &= \sqrt{v^2 + r_o^2} \\ \\
s &= \sqrt{v_a^2 + \left(\frac{a}{2}\right)^2}
\end{aligned}
$$
višina stranske ploskve
$$
\begin{aligned}
v_a &= \frac{v}{\sin\alpha_2} \\ \\
v_a &= \sqrt{v^2 + r_v^2} \\ \\
v_a &= \sqrt{s^2 - \left(\frac{a}{2}\right)^2}
\end{aligned}
$$
očrtana krožnica (polmer)
$$
\begin{aligned}
&r_o = \frac{a}{2\cdot\sin\frac{180^\circ}{n}} \\ \\
& n = 3 \ \Rightarrow \ r_o = \frac{a}{\sqrt{3}} \\ \\
& n = 4 \ \Rightarrow \ r_o = \frac{a}{\sqrt{2}}
\end{aligned}
$$
včrtana krožnica (polmer)
$$
\begin{aligned}
&r_v = \frac{a}{2\cdot\tan\frac{180^\circ}{n}} \\ \\
& n = 3 \ \Rightarrow \ r_v = \frac{\sqrt{3}}{6}a \\ \\
& n = 4 \ \Rightarrow \ r_v = \frac{a}{2}
\end{aligned}
$$
