The square Pyramid

The following elements of a square pyramid are calculated if two of them are given:

Example 1:

Given:
¯¯¯¯¯
            Edge  a = 1
        Volume  V = 1
		
Results:
¯¯¯¯¯¯¯
 Lateral edge  s = 3,082207
        Altitude h1 = 3
      Apothem h2 = 3,0413813
        Surface  S = 7,0827625
             Face  A = 1,5206906

Example 2:

Given:
¯¯¯¯¯
        Volume  V = 1
        Surface  S = 10

1st solution:
¯¯¯¯¯¯¯¯¯
            Edge  a = 2,1469752
 Lateral edge  s = 1,6517658
        Altitude h1 = 0,65082948
      Apothem h2 = 1,2553703
             Face  A = 1,3476244

2nd solution:
¯¯¯¯¯¯¯¯¯¯
            Edge  a = 0,62489814
 Lateral edge  s = 1,6517658
        Altitude h1 = 7,6825039
      Apothem h2 = 1,6219451
             Face  A = 0,50677523

See also:

Graphics 3D