Triangles in Pentagons

The following pictures show n unit squares packed inside the smallest known pentagon (with side s).

1.
           2.
           3.
s = cos(42°) / cos(18°)
s = .781+
Trivial.
  		s = √(6/(3+√5))
s = 1.070+
Found by Erich Friedman
in March 2012. 		s = 1.143+
Found by Maurizio Morandi
in August 2012.
 

4.
           5.
           6.
s = 1.199+
Found by Maurizio Morandi
in July 2012.
  		s = 1 + 2sin(12°)/√3
s = 1.240+
Found by Erich Friedman
in March 2012. 		s = 1.394+
Found by Timo Berthold et al
in January 2026.

7.
           8.
           9.
s = 1.581+
Found by David W. Cantrell
in July 2012. 		s = 1.659+
Found by Maurizio Morandi
in July 2012. 		s = 1.767+
Found by Maurizio Morandi in July 2012.
Improved slightly by David W. Cantrell in August 2012.

10.
           11.
           12.
s = 1.815+
Found by Timo Berthold et al
in January 2026. 		s = 1.871+
Found by Timo Berthold et al
in January 2026. 		s = 1.978+
Found by Timo Berthold et al
in January 2026.

13.
           14.
s = 2.017+
Found by Timo Berthold et al
in January 2026. 		s = 2.090+
Found by Timo Berthold et al
in January 2026.