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+
Trivial.
  		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 = 1.973+
Found by Ignacio Vallejo
in March 2026.

13.
           14.
           15.
s = 2.017+
Found by Timo Berthold et al
in January 2026. 		s = 2.088+
Found by Ignacio Vallejo
in April 2026. 		s = 2.123+
Found by Ignacio Vallejo
in March 2026.

16.
           17.
           18.
s = 2.176+
Found by Ignacio Vallejo
in March 2026. 		s = 2.237+
Found by Ignacio Vallejo
in March 2026. 		s = 2.294+
Found by Ignacio Vallejo
in March 2026.

19.
           20.
           21.
s = 2.344+
Found by Ignacio Vallejo
in March 2026. 		s = 2.434+
Found by Ignacio Vallejo
in March 2026. 		s = 2.479+
Found by Ignacio Vallejo
in March 2026.

22.
           23.
           24.
s = 2.570+
Found by Ignacio Vallejo
in March 2026. 		s = 2.620+
Found by Ignacio Vallejo
in March 2026. 		s = 2.667+
Found by Ignacio Vallejo
in March 2026.

25.
           26.
           27.
s = 2.720+
Found by Ignacio Vallejo
in March 2026. 		s = 2.771+
Found by Ignacio Vallejo
in March 2026. 		s = 2.820+
Found by Ignacio Vallejo
in March 2026.

28.
           29.
           30.
s = 2.868+
Found by Ignacio Vallejo
in March 2026. 		s = 2.903+
Found by Ignacio Vallejo
in April 2026. 		s = 2.952+
Found by Ignacio Vallejo
in April 2026.