Its complicated. There wasn't just one Hubble Ultra Deep Field (UDF) observation, but several, taken at different times, with different instruments, but pointed in (almost) the same direction.
The first image you refer to was taken with the WFC Infra red camera in 2009, in near infrared bands (1-1.6 microns). The area covered by this camera is $2.4$ arminutes on a side. i.e. 5.76 square arcminutes.
The second Beckwith et al. (2005) paper you refer to, discusses a UDF taken with the Advanced Camera for Surveys (ACS) in 2004, an instrument that works in the visible part of the spectrum, edging just into the near infrared (300-900nm). The image is approximately square because it had to be taken using different roll angles of the spacecraft and the image was dithered. The final (cropped) square image is 11 square arcminutes.
There is then a 2012 Hubble UDF taken again with the WFC IR instrument, in the same direction, with increased exposure times, especially in the 1.05 micron band, and added a 1.4 micron deep image. This also covers 5.76 square arcminutes. It also added further exposure (another 128 orbits!) to the 800nm optical/near IR exposure with the ACS instrument (11 square arcminutes). http://adsabs.harvard.edu/abs/2013ApJS..209....3K
EDIT: The number of square degrees on the sky is $4\pi (180/\pi)^2 =$ 41253 square degrees, which gives your number.