Squares in Pentagons

The following pictures show n squares packed inside a unit pentagon, so that the total sum of the sides of the squares is as large as possible.

1.
           2.
           3.
Σ s = cos(18°)/cos(27°) = 1.06740+
Trivial.
  		Σ s = 1.39526+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.79081+
Found by Jonathan Viquerat
in June 2026.

4.
           5.
           6.
Σ s = 2.20338+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.56933+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.86825+
Found by Jonathan Viquerat
in June 2026.

7.
           8.
           9.
Σ s = 3.07742+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 3.31577+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 3.52833+
Found by Jonathan Viquerat
in June 2026.

10.
           11.
           12.
Σ s = 3.74075+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 4.00392+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 4.17341+
Found by Jonathan Viquerat
in June 2026.

13.
           14.
           15.
Σ s = 4.35536+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 4.56549+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 4.73074+
Found by Pedro Martins
in July 2026.

16.
           17.
           18.
Σ s = 4.89463+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.03511+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.19478+
Found by Jonathan Viquerat
in June 2026.

19.
           20.
           21.
Σ s = 5.33987+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.49375+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.61319+
Found by Joost de Winter
in October 2026.

22.
           23.
           24.
Σ s = 5.77198+
Found by Joost de Winter
in September 2026. 		Σ s = 5.91403+
Found by Joost de Winter
in September 2026. 		Σ s = 6.02151+
Found by Joost de Winter
in September 2026.

25.
           26.
           27.
Σ s = 6.19566+
Found by Joost de Winter
in September 2026. 		Σ s = 6.36854+
Found by Joost de Winter
in September 2026. 		Σ s = 6.45438+
Found by Joost de Winter
in September 2026.

28.
           29.
           30.
Σ s = 6.56765+
Found by Joost de Winter
in October 2026. 		Σ s = 6.66961+
Found by Joost de Winter
in October 2026. 		Σ s = 6.81748+
Found by Joost de Winter
in October 2026.

31.
           32.
           33.
Σ s = 6.95378+
Found by Joost de Winter
in September 2026. 		Σ s = 7.02863+
Found by Joost de Winter
in October 2026. 		Σ s = 7.15817+
Found by Joost de Winter
in September 2026.

34.
           35.
           36.
Σ s = 7.28588+
Found by Joost de Winter
in September 2026. 		Σ s = 7.36445+
Found by Joost de Winter
in October 2026. 		Σ s = 7.48344+
Found by Joost de Winter
in September 2026.

37.
           38.
           39.
Σ s = 7.61256+
Found by Joost de Winter
in September 2026. 		Σ s = 7.69681+
Found by Joost de Winter
in October 2026. 		Σ s = 7.81122+
Found by Joost de Winter
in September 2026.

40.
           41.
           42.
Σ s = 7.95744+
Found by Joost de Winter
in September 2026. 		Σ s = 8.01516+
Found by Joost de Winter
in October 2026. 		Σ s = 8.10463+
Found by Joost de Winter
in October 2026.

43.
           44.
           45.
Σ s = 8.22295+
Found by Joost de Winter
in September 2026. 		Σ s = 8.28067+
Found by Joost de Winter
in October 2026. 		Σ s = 8.35300+
Found by Joost de Winter
in October 2026.

46.
           47.
           48.
Σ s = 8.47185+
Found by Joost de Winter
in September 2026. 		Σ s = 8.52956+
Found by Joost de Winter
in October 2026. 		Σ s = 8.59006+
Found by Joost de Winter
in October 2026.

49.
           50.
Σ s = 8.70827+
Found by Joost de Winter
in September 2026. 		Σ s = 8.76599+
Found by Joost de Winter
in October 2026.