Using the .NET API, the Location (AnnotationRectangle) for a TextEntry annotation has a position (Top, Left), but the dimensions (Width, Height) end up both as 0. If the TextEntry annotation is set using the web client or using the Platform API, you seem to get the same result - always 0. The web client does seem to understand what the size of the rectangle that you're typing in, however, and adds CR/LF at the right spots to get multi-line text to "fit" into the text area rectangle. But if you use the Platform API, you have to insert the CR/LF yourself to prevent long text annotations from running off the page. Is that a bug or by design? If the TextEntry Location were really designed to use only the Top and Left parts of the AnnotationRectangle, one would have expected the example for placing the TextEntry annotation to have zeros for the Height and Width.
(Observed using 7.1 and 7.4)