Regular Triangular Pyramid Calculator

Name: Regular Triangular Pyramid - Geometry Calculator
Author: Jürgen Kummer

Calculations at a regular triangular pyramid. This is a regular pyramid to the base 3, respectively a general tetrahedron wtih an equilateral triangle as base and three equal isosceles triangles with base a and legs b as side faces. With a=b, this is a regular tetrahedron.
Enter two values of base length, edge length and height. Choose the number of decimal places, then click Calculate.

Formulas:

b^{2} = h^{2} + \frac{a^{2}}{3}

s = \sqrt{\frac{4 b^{2} - a^{2}}{4}}

A = \frac{\sqrt{3}}{4} \cdot a^{2} + \frac{3}{2} \cdot a \cdot s

V = \frac{\sqrt{3}}{12} \cdot a^{2} \cdot h

Lengths and heights have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

The regular triangular pyramid has three planes of symmetry. These each pass through an edge b and through the middle of the opposite side a. It is rotationally symmetrical to the axis through the center of the equilateral triangle and the vertex at an angle of 120 degrees and multiples thereof.
A regular triangular pyramid is the simplest of all regular pyramids. Much more well-known and widespread, however, is the square pyramid, which is often what is meant when one just says pyramid. Buildings very rarely have a triangular base and therefore regular triangular pyramids are scarcely found in architecture. An example of a structure in this form is the Tetrahedron of Bottrop, a skeleton-like tower that serves as an observation platform. This has a base length of around 60 meters. The entire structure is 58 meters high, but rests on 8-meter-high concrete pillars, so that the height of the pyramid is 50 meters. This would result in an edge length of the steep edges of just under 61 meters, if the previous information is correct. So it would not be quite a regular tetrahedron, but actually just a regular triangular pyramid. Unfortunately, no exact values can be found, but for an example calculation this doesn't matter.

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