What is the area of the sky that is covered by the Hubble Ultra Deep Field image?

Your method is correct. When the angle is "small" so that we can ignore curvature, then the rectangular solid angle is just the product of the two side angles. (This doesn't hold for "large" angles).

I cannot find a perfect explanation, but one source of this confusion may be that the UDF was imaged by two separate instruments, one optical, one infrared.

This page shows some details, including the fact that the optical survey is 3 arcminutes square and the IR is 2.4 arcminutes square. So I think the entire UDF is 11 square arcminutes (3.4 arcminutes square), but the image released does not cover the entire area.

An additional piece I found that supports this size is that the Hubble ACS wide-field channel (found here) is 202 arcseconds on a side, and this page (which has an image showing the relative size of the moon, the HUDF and some other Hubble surveys) states the HUDF is exactly the size of one wide-field image. 202 arcseconds squared is 11.3 square arcminutes.