Triangles in Squares

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

1.
           2.
           3.
Σ s = √6–√2 = 1.03527+
Trivial.
  		Σ s = 2√6/3 = 1.63299+
Trivial.
A continuum of solutions. 		Σ s = 2.09499+
Found by Jonathan Viquerat
in June 2026.

4.
           5.
           6.
Σ s = 6–2√3 = 2.53590+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.85406+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 3.19936+
Found by Jonathan Viquerat
in June 2026.

7.
           8.
           9.
Σ s = 3.51037+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 3.84531+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 4.06910+
Found by Jonathan Viquerat
in June 2026.

10.
           11.
           12.
Σ s = 4.27964+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 4.54529+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 4.77454+
Found by Jonathan Viquerat
in June 2026.

13.
           14.
           15.
Σ s = 5.03476+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.27330+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.42874+
Found by Jonathan Viquerat
in June 2026.

16.
           17.
           18.
Σ s = 5.65499+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.81278+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 6.03574+
Found by Jonathan Viquerat
in June 2026.

19.
           20.
Σ s = 6.21461+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 6.34299+
Found by Jonathan Viquerat
in June 2026.