Pyramid calculation

Description and formulas for the calculation of pyramids

Pyramid Definition

  • 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 sides of a pyramid are triangular. They run inwards from the bases and meet at the top.

Formulas for the calculation of pyramids

The following formulas refer to the calculation of a right quadrangular pyramid

Calculate base side length \(a\) of a pyramid

\(\displaystyle a=\sqrt{\frac{P}{4}}\)

Calculate radius to a side \(r_s\) of a pyramid

\(\displaystyle r_s=\sqrt{\frac{A}{2}}\)

Calculate radius to a vertex \(r_v\) of a pyramid

\(\displaystyle r_v=\sqrt{(a/2)^2+{r_s}^2}\)

Calculate perimeter of the base \(P\) of a pyramid

\(\displaystyle P=4·a\)

Calculate base area \(A\) of a pyramid

\(\displaystyle A=a^2\)

Calculate height \(h\) of a pyramid

\(\displaystyle h=\frac{3·V}{A} \)

\(\displaystyle h=\sqrt{m^2-{r_s}^2}\)

Calculate slant height \(m\) of a pyramid

\(\displaystyle m=\sqrt{h^2+{r_s}^2}\)

Calculate edge length \(k\) of a pyramid

\(\displaystyle k=\sqrt{m^2+(a^2/4)}\)

Calculate area of a slope \(M_1\) of a pyramid

\(\displaystyle M_1=\frac{m · a}{2}\)

Calculate lateral area \(M\) of a pyramid

\(\displaystyle M=\frac{m · P}{2}\)

Calculate volumen \(V\) of a pyramid

\(\displaystyle V=\frac{A · h}{3}\)