L's in Hexagons

L's in Hexagons The following pictures show n L's with short side 1 inside the smallest known hexagon (of side s).

1.

s = 2√((11 + 6√3)/39) = 1.481+
Trivial.
2.

s = 12^1/4 = 1.861+
Found by Maurizio Morandi
in May 2026. 3.

s = 1/2 + √3 = 2.232+
Found by Maurizio Morandi
in May 2026.

4.

s = 2.50337+
Found by Jake Loyd
in June 2026. 5.

s = 2.85988+
Found by Jake Loyd
in May 2026 6.

s = 3.04254+
Found by Jake Loyd
in June 2026.

7.

s = 3.25359+
Found by Jake Loyd
in June 2026. 8.

s = 2√3 = 3.464+
Trivial.
9.

s = 3.65374+
Found by Jake Loyd
in June 2026.

10.

s = 3.80531+
Found by Jake Loyd
in June 2026. 11.

s = 7/√3 = 4.041+
Trivial.
12.

s = 4.15868+
Found by Jake Loyd
in June 2026.

13.

s = 4.33273+
Found by Jake Loyd
in June 2026. 14.

s = 4.46716+
Found by Jake Loyd
in June 2026. 15.

s = 8/√3 = 4.61880+
Trivial.

16.

s = 4.72806+
Found by Aapo Lipponen
in July 2026. 17.

s = 4.93064+
Found by Aaden Abraham
in July 2026. 18.

s = 5.09795+
Found by Aapo Lipponen
in July 2026.

           19.

s = 3√3 = 5.19615+
Found by Maurizio Morandi
in July 2026.            20.

s = 2+17√3/9 = 5.27165+
Found by Maurizio Morandi
in August 2026.            21.

s = (13+5√3)/4 = 5.41506+
Found by Maurizio Morandi
in July 2026.

           22.

s = 7(1+1/√3)/2 = 5.52072+
Found by Maurizio Morandi
in August 2026.            23.

s = 7√6/3 = 5.71547+
Found by Aaden Abraham
in July 2026.            24.

s = 10/√3 = 5.77350+
Found by Aaden Abraham
in July 2026.

           25.

s = 7/2+4/√3 = 5.80940++
Found by Maurizio Morandi
in August 2026.            26.

s = 9/2+5√3/6 = 5.94337+
Found by Maurizio Morandi
in August 2026.            27.

s = 9/2+11√3/12 = 6.08771+
Found by Maurizio Morandi
in July 2026.

           28.

s = 7/2+19√/12 = 6.24241+
Found by Maurizio Morandi
in July 2026.            29.

s = 11/√3 = 6.35085+
Found by Aaden Abraham
in July 2026.            30.

s = (11+√3)/2 = 6.36602+
Found by Maurizio Morandi
in July 2026.