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 = 1.86834+
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 = 5.34770+
Found by Jonathan Viquerat
in October 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 = 6.31699+
Found by Joost de Winter
in October 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 = 7.17437+
Found by Jonathan Viquerat
in October 2026.

16.
           17.
           18.
Σ s = 7.48786+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 7.74732+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 7.96356+
Found by Jonathan Viquerat
in October 2026.

19.
           20.
           21.
Σ s = 8.22207+
Found by Joost de Winter
in October 2026. 		Σ s = 8.51465+
Found by Pedro Martins
in July 2026. 		Σ s = 8.65807+
Found by Jonathan Viquerat
in October 2026.

22.
           23.
           24.
Σ s = 8.89359+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 9.06340+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 9.27320+
Found by Joost de Winter
in October 2026.

25.
           26.
           27.
Σ s = 9.46826+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 9.66343+
Found by Pedro Martins
in October 2026. 		Σ s = 9.85993+
Found by Pedro Martins
in October 2026.

28.
           29.
           30.
Σ s = 10.04286+
Found by Pedro Martins
in October 2026. 		Σ s = 10.24927+
Found by Pedro Martins
in October 2026. 		Σ s = 10.43887+
Found by Joost de Winter
in October 2026.

31.
           32.
           33.
Σ s = 10.62546+
Found by Pedro Martins
in October 2026. 		Σ s = 10.78799+
Found by Pedro Martins
in October 2026. 		Σ s = 10.97649+
Found by Pedro Martins
in October 2026.

34.
           35.
           36.
Σ s = 11.14702+
Found by Pedro Martins
in October 2026. 		Σ s = 11.32301+
Found by Joost de Winter
in October 2026. 		Σ s = 11.49407+
Found by Joost de Winter
in October 2026.

37.
           38.
           39.
Σ s = 11.66499+
Found by Pedro Martins
in October 2026. 		Σ s = 11.83386+
Found by Pedro Martins
in October 2026. 		Σ s = 12.01613+
Found by Pedro Martins
in October 2026.

40.
           41.
           42.
Σ s = 12.19203+
Found by Joost de Winter
in October 2026. 		Σ s = 12.32065+
Found by Joost de Winter
in October 2026. 		Σ s = 12.50118+
Found by Pedro Martins
in October 2026.

43.
           44.
           45.
Σ s = 12.64015+
Found by Pedro Martins
in October 2026. 		Σ s = 12.81525+
Found by Pedro Martins
in October 2026. 		Σ s = 12.98616+
Found by Joost de Winter
in October 2026.

46.
           47.
           48.
Σ s = 13.09197+
Found by Pedro Martins
in October 2026. 		Σ s = 13.25878+
Found by Joost de Winter
in October 2026. 		Σ s = 13.36774+
Found by Joost de Winter
in October 2026.

49.
           50.
Σ s = 13.53192+
Found by Pedro Martins
in October 2026. 		Σ s = 13.64753+
Found by Pedro Martins
in October 2026.