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.
Σ s = 3.03275 +
Found by Haowei Lin
in July 2026. 		Σ s = 3.11736+
Found by Haowei Lin
in July 2026.