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 = 121/4 = 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 = 4.95+
Found by Aaden Abraham
in July 2026. 		           18.

s = 5.175+
Found by Aaden Abraham
in July 2026.

           19.

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

s = (9+√3)/2 = 5.36602+
Found by Aaden Abraham
in July 2026. 		           21.

s = 7(1+1/√3)/2 = 5.52072+
Found by Aaden Abraham
in July 2026.