volume
$$ V = \frac{1}{3} S_b \cdot h $$
superficie totale
$$ S_t = S_b + S_{l} $$
superficie di base
$$
\begin{aligned}
&S_b = \frac{1}{4} n a^2 \cot\frac{180^\circ}{n} \\ \\
& n = 3 \ \Rightarrow \ S_b = \frac{\sqrt{3}}{4} a^2 \\ \\
& n = 4 \ \Rightarrow \ S_b = a^2
\end{aligned}
$$
superficie laterale
$$ S_{l} = \frac{na a_p}{2} $$
spigolo laterale
$$
\begin{aligned}
s &= \frac{h}{\sin\alpha_1} \\ \\
s &= \sqrt{h^2 + R^2} \\ \\
s &= \sqrt{a_p^2 + \left(\frac{a}{2}\right)^2}
\end{aligned}
$$
altezza
$$
\begin{aligned}
a_p &= \frac{h}{\sin\alpha_2} \\ \\
a_p &= \sqrt{h^2 + r^2} \\ \\
a_p &= \sqrt{a^2 - \left(\frac{a}{2}\right)^2}
\end{aligned}
$$
cerchio circoscritto (raggio)
$$
\begin{aligned}
&R = \frac{a}{2\cdot\sin\frac{180^\circ}{n}} \\ \\
& n = 3 \ \Rightarrow \ R = \frac{a}{\sqrt{3}} \\ \\
& n = 4 \ \Rightarrow \ R = \frac{a}{\sqrt{2}}
\end{aligned}
$$
cerchio inscritto (raggio)
$$
\begin{aligned}
&r = \frac{a}{2\cdot\tan\frac{180^\circ}{n}} \\ \\
& n = 3 \ \Rightarrow \ r = \frac{\sqrt{3}}{6}a \\ \\
& n = 4 \ \Rightarrow \ r = \frac{a}{2}
\end{aligned}
$$