Squares Covering Squares

The following pictures show n unit squares covering the largest known square (of area A). For the n not pictured, the trivial covering (with no tilted squares) is the best known.

3.
           7.
           8.
A = 1/2 + √5/2 = 1.61803+
Found by Dudeney
in 1931. 		A = 11/4 + 3/√2 = 4.87132+
Found by Trevor Green
in September 2000. 		A = 3 + 2√2 = 5.82842+
Found by Trevor Green
in September 2000.

12.
           13.
           14.
A = 9.09558+
Found by Abdulfayyod Mukhamedov
in September 2026. 		A = 11/2 + 3√2 = 9.74264+
Found by David Paterson
in July 2002. 		A = 10.86482+
Found by Abdulfayyod Mukhamedov
in September 2026.

15.
           21.
           22.
A = 11.84721+
Found by Ryan Chi
in September 2026. 		A = 17/2 + 6√2 = 16.98528+
Found by David Paterson
in July 2002. 		A = 17.821+
Found by David Cantrell
in August 2002.

23.
           24.
           31.
A = 19.02461+
Found by Abdulfayyod Mukhamedov
in September 2026. 		A = 20.008+
Found by Maurizio Moranndi
in October 2010. 		A = 25.527+
Found by David Paterson
in September 2002.

32.
           33.
           34.
A = 83/4 + 9/√2 = 27.11396+
Found by David Paterson
in September 2002. 		A = 27.988+
Found by Maurizio Morandi
in October 2010. 		A = 18 + 8√2 = 29.31370+
Found by David Paterson
in September 2002.

35.
           43.
           44.
A = 30.29821+
Found by Ryan Chi and d/dx
in September 2026. 		A = 36.608+
Found by David Paterson
in September 2002. 		A = 41/2 + 12√2 = 37.47056+
Found by David Paterson
in September 2002.

45.
           46.
           47.
A = 39.042+
Found by David Paterson
in September 2002. 		A = 39.77036+
Found by Ryan Chi and d/dx
in September 2026. 		A = 41.34484+
Found by Ryan Chi and d/dx
in September 2026.

48.
A = 42.69367+
Found by Ryan Chi and d/dx
in September 2026.