MatheAss 9.0Geometry 3D

The regular Prism

A regular Prism has a regular polygon as base and vertical edges.

The following elements of a regular prism are calculated if two of them are given:

 

Example 1:

Given:
¯¯¯¯¯¯
          Vertices  n = 4
          Volume  V = 1
          Surface  S = 6

Results:
¯¯¯¯¯¯¯
               Edge  a = 1
           Altitude  h = 1
  Circumradius rc = 0,70710678
           Inradius ri = 0,5
              Base  B = 1

Example 2:

Given:
¯¯¯¯¯¯
          Vertices  n = 4
          Volume  V = 1
          Surface  S = 10

1st solution:
¯¯¯¯¯¯¯¯¯¯
               Edge  a = 0,41421356
           Altitude  h = 5,8284272
  Circumradius rc = 0,29289322
           Inradius ri = 0,20710678
              Base  B = 0,17157287

2nd solution:
¯¯¯¯¯¯¯¯¯¯
               Edge  a = 2
           Altitude  h = 0,25
  Circumradius rc = 1,4142136
           Inradius ri = 1
              Base  B = 4

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