Pentagons in Squares

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

1.
           2.
           3.
Σ s = √(8–2radic;(10+2√5)) = .62573+
Trivial.
  		Σ s = .81187+
Trivial.
A continuum of solutions. 		Σ s = 1.08249+
Found by Jonathan Viquerat
in June 2026.

4.
           5.
           6.
Σ s = 1.33718+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.46940+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.61106+
Found by Jonathan Viquerat
in June 2026.

7.
           8.
           9.
Σ s = 1.75771+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.91200+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.04259+
Found by Jonathan Viquerat
in June 2026.

10.
           11.
           12.
Σ s = 2.15626+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.26772+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.38481+
Found by Jonathan Viquerat
in June 2026.

13.
           14.
           15.
Σ s = 2.48116+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.57744+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.67893+
Found by Haowei Lin
in July 2026.

16.
           17.
           18.
Σ s = 2.77352+
Found by Haowei Lin
in July 2026. 		Σ s = 2.85448+
Found by Haowei Lin
in July 2026. 		Σ s = 2.94080+
Found by Haowei Lin
in July 2026.

19.
           20.
           21.
Σ s = 3.03275+
Found by Haowei Lin
in July 2026. 		Σ s = 3.11736+
Found by Haowei Lin
in July 2026. 		Σ s = 3.18115+
Found by Joost de Winter
in September 2026.

22.
           23.
           24.
Σ s = 3.20077+
Found by Joost de Winter
in September 2026. 		Σ s = 3.30377+
Found by Joost de Winter
in September 2026. 		Σ s = 3.40330+
Found by Joost de Winter
in September 2026.

25.
           26.
           27.
Σ s = 3.47558+
Found by Joost de Winter
in September 2026. 		Σ s = 3.54918+
Found by Joost de Winter
in September 2026. 		Σ s = 3.61647+
Found by Joost de Winter
in September 2026.

28.
           29.
           30.
Σ s = 3.70147+
Found by Joost de Winter
in September 2026. 		Σ s = 3.73109+
Found by Joost de Winter
in September 2026. 		Σ s = 3.82705+
Found by Joost de Winter
in September 2026.

31.
           32.
           33.
Σ s = 3.87081+
Found by Joost de Winter
in September 2026. 		Σ s = 3.94532+
Found by Joost de Winter
in September 2026. 		Σ s = 4.01176+
Found by Joost de Winter
in September 2026.

34.
           35.
           36.
Σ s = 4.04708+
Found by Joost de Winter
in September 2026. 		Σ s = 4.13847+
Found by Joost de Winter
in September 2026. 		Σ s = 4.19149+
Found by Joost de Winter
in September 2026.

37.
           38.
           39.
Σ s = 4.26608+
Found by Joost de Winter
in September 2026. 		Σ s = 4.31764+
Found by Joost de Winter
in September 2026. 		Σ s = 4.36402+
Found by Joost de Winter
in September 2026.

40.
           41.
           42.
Σ s = 4.44004+
Found by Joost de Winter
in September 2026. 		Σ s = 4.50877+
Found by Joost de Winter
in September 2026. 		Σ s = 4.55809+
Found by Joost de Winter
in September 2026.

43.
           44.
           45.
Σ s = 4.59665+
Found by Joost de Winter
in September 2026. 		Σ s = 4.62311+
Found by Joost de Winter
in September 2026. 		Σ s = 4.69999+
Found by Joost de Winter
in September 2026.

46.
           47.
           48.
Σ s = 4.77437+
Found by Joost de Winter
in September 2026. 		Σ s = 4.81502+
Found by Joost de Winter
in September 2026. 		Σ s = 4.88079+
Found by Joost de Winter
in September 2026.

49.
           50.
Σ s = 4.93921+
Found by Joost de Winter
in September 2026. 		Σ s = 4.96864+
Found by Joost de Winter
in September 2026.