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 
  • Radius to a side
rs    
       
Regardless of the number of corners of the pyramid, the radius to a corner can be calculated with the following formula.
  • Radius to a vertex
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
 
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Points, Distance and Midpoint
Distance Between Two Points
Lines and Gradiants
Angle Definition and Relationships
Lines and Segments of Triangles
Right-Triangles and Pythagorean
Circle
Square
Rectangle
Rhombus
Rhomboid
Trapezoid

Cone
Pyramid
Sphere
Spherical Segments and Sectors
 

   



           
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