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.
A = 1/2 + √5/2 = 1.618+
Found by Dudeney
in 1931. 		A = 11/4 + 3/√2 = 4.871+
Found by Trevor Green
in September 2000.

8.            13.
A = 3 + 2√2 = 5.828+
Found by Trevor Green
in September 2000. 		A = 11/2 + 6/√2 = 9.742+
Found by David Paterson
in July 2002.

14.            15.
A = 10.860+
Found by Michael Kearney
in July 2002. 		A = 11.806+
Found by Maurizio Morandi
in October 2010.

21.            22.
A = 17/2 + 6√2 = 16.985+
Found by David Paterson
in July 2002. 		A = 17.821+
Found by David Cantrell
in August 2002.

23.            24.
A = 19.001+
Found by David Cantrell
in July 2002. 		A = 20.008+
Found by Maurizio Moranndi
in October 2010.

31.            32.
A = 25.527+
Found by David Paterson
in September 2002. 		A = 83/4 + 9/√2 = 27.113+
Found by David Paterson
in September 2002.

33.            34.
A = 27.988+
Found by Maurizio Morandi
in October 2010. 		A = 18 + 8√2 = 29.313+
Found by David Paterson
in September 2002.

35.            43.
A = 30.247+
Found by Maurizio Morandi
in October 2010. 		A = 36.608+
Found by David Paterson
in September 2002.

44.            45.
A = 41/2 + 24/√2 = 37.470+
Found by David Paterson
in September 2002. 		A = 39.042+
Found by David Paterson
in September 2002.