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 = 5.67685+
Found by Pedro Martins
in July 2026. 		Σ s = 5.99822+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 6.31483+
Found by Pedro Martins
in July 2026.

13.
           14.
           15.
Σ s = 6.59263+
Found by Pedro Martins
in July 2026. 		Σ s = 6.91179+
Found by Pedro Martins
in July 2026. 		Σ s = 7.17406+
Found by Pedro Martins
in July 2026.

16.
           17.
           18.
Σ s = 7.48785+
Found by Pedro Martins
in July 2026. 		Σ s = 7.74731+
Found by Pedro Martins
in July 2026. 		Σ s = 7.91451+
Found by Jiří Minarčík
in August 2026.

19.
           20.
Σ s = 8.18204+
Found by Pedro Martins
in July 2026. 		Σ s = 8.51465+
Found by Pedro Martins
in July 2026.