Description and formulas for the calculation of pyramids
The base of a pyramid is a polygon with at least three edges.
The number of edges of the base determines the number of slopes of the pyramid.
The following formulas refer to the calculation of a right quadrangular pyramid
\(\displaystyle a=\sqrt{\frac{P}{4}}\)
\(\displaystyle r_s=\sqrt{\frac{A}{2}}\)
\(\displaystyle r_v=\sqrt{(a/2)^2+{r_s}^2}\)
\(\displaystyle P=4·a\)
\(\displaystyle A=a^2\)
\(\displaystyle h=\frac{3·V}{A} \)
\(\displaystyle h=\sqrt{m^2-{r_s}^2}\)
\(\displaystyle m=\sqrt{h^2+{r_s}^2}\)
\(\displaystyle k=\sqrt{m^2+(a^2/4)}\)
\(\displaystyle M_1=\frac{m · a}{2}\)
\(\displaystyle M=\frac{m · P}{2}\)
\(\displaystyle V=\frac{A · h}{3}\)