Triangles in Pentagons

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

1.
           2.
           3.
Σ s = cos(18°)/cos(42°) = 1.27977+
Trivial.
  		Σ s = (1+√5)/√3 = 1.86835+
Trivial
A continuum of solutions. 		Σ s = 2.68270+
Found by Jonathan Viquerat
in June 2026.

4.
           5.
           6.
Σ s = 3.37307+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 15/(3+2√3sin(12˚)) = 4.03202+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 4.33548+
Found by Jonathan Viquerat
in June 2026.

7.
           8.
           9.
Σ s = 4.67519+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.01502+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.34505+
Found by Jonathan Viquerat
in June 2026.

10.
           11.
           12.
Σ s = 5.66473+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5.99822+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 6.22089+
Found by Jonathan Viquerat
in June 2026.

13.
           14.
           15.
Σ s = 6.56013+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 6.74885+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 7.03011+
Found by Jonathan Viquerat
in June 2026.

16.
           17.
           18.
Σ s = 7.13938+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 7.72391+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 7.48967+
Found by Jonathan Viquerat
in June 2026.

19.
           20.
Σ s = 7.91638+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 8.01153+
Found by Jonathan Viquerat
in June 2026.