RedCrab Math Tutorial

Pyramid Calculation

• 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

Pyramid Formulas

The following table shows the formulas for calculating the properties of a pyramid.

• Number of sides
n
• Base sides
a

For a square pyramid, the radius to a side, is the half length of the side
rs

Regardless of the number of corners of the pyramid, the radius to a corner can be calculated with the following formula.
rv rv = √(a/2)² + rs²

The perimeter of the base of the pyramid is the sum of the lengths of all sides. The example below only applies to square bases.
• perimeter of base
P 4·a

The calculation of the base area of the pyramid depends on its shape. The example below is for a square base only *)
• Base
A a² *)

The height of the pyramid can be calculated from the volume and the base area, or from the slant height and the radius to a side of the base.
• Height
h h = (3·V) / A h = √m² - rs²

Calculate the slant height of a pyramid from pyramid height and radius to the side of the base.
• Slant Height
m m = √h² + rs²

Calculation of the edge length of a pyramid from the slant height and the side length
• Edge Lenght
k k = √m² + (a² / 4)

The of a slope can be calculated from the slant height and the side length of the base.
• Area of a slope
M1 M1 = (m · a) / 2

The lateral surface of the pyramid can be calculated from the slant height of the pyramid and the side length of the base. The n in the following formula represents the number of pages.
• Lateral area
M M = (m · P) / 2 M = (m · a · n ) / 2

Calculation of the volume of a pyramid from the base and the height
• Volume
V V = (A · h) / 3

Example with RedCrab Calculator
• The calculation uses the class Pyramid