What is the circumference of a pyramid

Formula overview pyramid

Reading time: 12 min

In order to be able to describe a pyramid, there are a few terms that one must know. These include the well-known terms such as “outer surface”, “surface” and “volume”, but there are also the terms “side edge” or “height of the side surface”, especially for pyramids. A collection of all these terms and the associated formulas are shown in the following diagram.

Link to the graphic: https://www.matheretter.de/img/wiki/pyramide-formeln.png

The “straight square pyramid” we are looking at therefore consists of a square base with the base side a. The “straight pyramid” also indicates that the tip is exactly above the center of the base, which is described by the height h. Let's take a closer look at the formulas below, assuming that a and h are always given.

Scope u

The circumference also corresponds to that of a square and must also be specified.

 

Diagonal d

We already know the diagonal d from the squares. We have a square footprint here, and that's how it arises.

Height ha

Not only does the pyramid have a height in general, but the side faces also have a height. These triangular heights can be calculated with the help of and if one is looking for right triangles in order to be able to apply the Pythagorean theorem.

With the Pythagorean theorem it follows:

\ (h_a = \ sqrt {h ^ 2 + \ frac {a} {2} ^ 2} \)

Side edge / surface line see

The square pyramid has 4 side edges (also called surface lines). Here, too, the length can be expressed over and, if one again uses the Pythagorean theorem as an aid.

The triangle that you should recognize here is formed from the side you are looking for, the height and the. That represents half the diagonal of the base area, that is. If you now square, as the Pythagoras demands, you get.

This gives the formula:

Base G

The base area corresponds to that of a square and must also be specified.

 

Outer surface M

We have four isosceles triangles and can determine these with, where one triangle has the area.

 

Surface O

As usual, the surface is made up of the base and the outer surface. With that we have.

 

Volume V

The volume of a pyramid results in. The factor \ (\ frac {1} {3} \) can easily be illustrated using a cube. We have a cube with the edge length, i.e. the volume. 6 pyramids fit into this, the tips of which meet in the middle.

If you now imagine only half the cube, you have a volume of. If you look again in the graphic, it is clear that the height of a pyramid can also be specified. If we continue to look at the half cube, we know that it has to be, because in the half cube we no longer have six, but three pyramids. So it results for the pyramid.

Angles in pyramids

In the pyramid we find two angles, as shown in the following figure. For given sides, they can be calculated using the cosine law.