Calculations at a right square pyramid, a special case of the regular pyramid. Enter side length and height and choose the number of decimal places. Then click Calculate. See also general pyramid. The angle is calculated in degrees, here you can convert angle units.
Formulas:
s = √ a² / 4 + h²
e = √ a² / 2 + h²
α = arccos( ((a/2)² + s² - h²) / (a*s) )
A = a² + a * √ 4 * h² + a²
V = 1/3 * a² * h
Length and height 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 pyramid is of course known from the ancient Egyptian buildings of the same name, which also gave its name to the geometric shape. After step pyramids and a pyramid that was planned too steeply and then became a bent pyramid, the first pyramid in the known form was the Red Pyramid of Snefru from the 27th century BC. The largest is the Pyramid of Cheops, built a few decades later and measuring almost 140 meters high, around ten meters less than when it was originally built. The triangular pyramid, regular pyramids with equilateral polygons as the base and general pyramids with any polyhedra are also known as geometric pyramids. The triangular pyramid is also a special case of the general tetrahedron. If you cut the top of a pyramid straight, you get a square frustum, a regular frustum or a general frustum.
The straight, square pyramid is axially symmetrical to the two cutting planes through two opposite corners and the top and the two cutting planes through two opposite slant heights. So it has four symmetry planes. It is rotationally symmetrical with the number 4, i.e. at 90 degrees rotation along the height axis.