Calculations at a right regular pyramid. This is a pyramid with a regular n-gon as base. Right means, the apex is directly above the centroid of the base.
Enter side length, height and number of vertices of the base. Choose the number of decimal places, then click Calculate.
Formulas:
s = √ h² + 1/4 * a² * cot²( π/n )
e = √ s² + a² / 4
B = n * a² / ( 4 * tan(π/n) )
A = B + n * a * s / 2
V = 1/3 * B * h
pi:
π = 3.141592653589793...
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 most common regular pyramid is, of course, the square pyramid, known from the ancient Egyptians, who built such structures as tombs for pharaohs. The name pyramid, however, comes from Greek and describes such shapes. Pyramids with more than four corners at the base are much rarer. With three corners at the base, it is a triangular pyramid, which is a special tetrahedron. The more the number of corners is increased, the more the regular pyramid approaches a cone.
If the apex of a regular pyramid is cut straight off, you get a regular frustum. The regular pyramid is a special case of the general pyramid. Two identical regular pyramids, placed together at the base, form a regular bipyramid. The pyramid and the matching truncated pyramid, in turn, form a frustum pyramid.
The right, regular pyramid is mirror-symmetric about every plane passing through a vertex or edge of the base, through the directly opposite vertex or edge of the base, and through the apex. There are as many planes of symmetry as there are vertices or edges at the base; this number is denoted here as n. These pyramids are rotationally symmetric about an axis through the apex and the center of the base at an angle of 360 degrees divided by the number of vertices at the base.
