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 = 5.34505+
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 = 7.95750+
Found by Pedro Martins
in August 2026.

19.
           20.
           21.
Σ s = 8.20426+
Found by Joost de Winter
in September 2026. 		Σ s = 8.51465+
Found by Pedro Martins
in July 2026. 		Σ s = 8.63942+
Found by Joost de Winter
in September 2026.

22.
           23.
           24.
Σ s = 8.65903+
Found by Joost de Winter
in September 2026. 		Σ s = 8.92147+
Found by Joost de Winter
in September 2026. 		Σ s = 9.22519+
Found by Joost de Winter
in September 2026.

25.
           26.
           27.
Σ s = 9.40172+
Found by Joost de Winter
in September 2026. 		Σ s = 9.56749+
Found by Joost de Winter
in September 2026. 		Σ s = 9.68989+
Found by Joost de Winter
in September 2026.

28.
           29.
           30.
Σ s = 9.93448+
Found by Joost de Winter
in September 2026. 		Σ s = 10.04141+
Found by Joost de Winter
in September 2026. 		Σ s = 10.25213+
Found by Joost de Winter
in September 2026.

31.
           32.
           33.
Σ s = 10.55739+
Found by Joost de Winter
in September 2026. 		Σ s = 10.57199+
Found by Joost de Winter
in September 2026. 		Σ s = 10.76384+
Found by Joost de Winter
in September 2026.

34.
           35.
           36.
Σ s = 11.01790+
Found by Joost de Winter
in September 2026. 		Σ s = 11.27617+
Found by Joost de Winter
in September 2026. 		Σ s = 11.34044+
Found by Joost de Winter
in September 2026.

37.
           38.
           39.
Σ s = 11.52216+
Found by Joost de Winter
in September 2026. 		Σ s = 11.69775+
Found by Joost de Winter
in September 2026. 		Σ s = 11.84630+
Found by Joost de Winter
in September 2026.

40.
           41.
           42.
Σ s = 12.02625+
Found by Joost de Winter
in September 2026. 		Σ s = 12.18641+
Found by Joost de Winter
in September 2026. 		Σ s = 12.26409+
Found by Joost de Winter
in September 2026.

43.
           44.
           45.
Σ s = 12.41424+
Found by Joost de Winter
in September 2026. 		Σ s = 12.48364+
Found by Joost de Winter
in September 2026. 		Σ s = 12.60998+
Found by Joost de Winter
in September 2026.

46.
           47.
           48.
Σ s = 12.79571+
Found by Joost de Winter
in September 2026. 		Σ s = 12.88900+
Found by Joost de Winter
in September 2026. 		Σ s = 13.07211+
Found by Joost de Winter
in September 2026.

49.
           50.
Σ s = 13.19577+
Found by Joost de Winter
in September 2026. 		Σ s = 13.32360+
Found by Joost de Winter
in September 2026.