부피
$$ V = \frac{1}{3} A_b \cdot h $$
겉넓이
$$ A = A_b + A_{l} $$
밑면의 넓이
$$
\begin{aligned}
&A_b = \frac{1}{4} n a^2 \cot\frac{180^\circ}{n} \\ \\
& n = 3 \ \Rightarrow \ A_b = \frac{\sqrt{3}}{4} a^2 \\ \\
& n = 4 \ \Rightarrow \ A_b = a^2
\end{aligned}
$$
옆면의 넓이
$$ A_{l} = \frac{n a h_a}{2} $$
옆면 모서리의 길이
$$
\begin{aligned}
s &= \frac{h}{\sin\alpha_1} \\ \\
s &= \sqrt{h^2 + R^2} \\ \\
s &= \sqrt{h_a^2 + \left(\frac{a}{2}\right)^2}
\end{aligned}
$$
높이
$$
\begin{aligned}
h_a &= \frac{h}{\sin\alpha_2} \\ \\
h_a &= \sqrt{h^2 + r^2} \\ \\
h_a &= \sqrt{l^2 - \left(\frac{a}{2}\right)^2}
\end{aligned}
$$
외접원 (반지름)
$$
\begin{aligned}
&R = \frac{a}{2\cdot\sin\frac{180^\circ}{n}} \\ \\
& n = 3 \ \Rightarrow \ R = \frac{a}{\sqrt{3}} \\ \\
& n = 4 \ \Rightarrow \ R = \frac{a}{\sqrt{2}}
\end{aligned}
$$
내접원 (반지름)
$$
\begin{aligned}
&r = \frac{a}{2\cdot\tan\frac{180^\circ}{n}} \\ \\
& n = 3 \ \Rightarrow \ r = \frac{\sqrt{3}}{6}a \\ \\
& n = 4 \ \Rightarrow \ r = \frac{a}{2}
\end{aligned}
$$
