Could I create a minipage with defined height? Yes, but it wouldn’t work the way I or you want.

For example here is a minipage with a defined height of 2cm:

\documentclass{article} \usepackage[showboxes,overlay]{textpos} \begin{document} \setlength{\parindent}{0cm} \TPshowboxestrue \begin{textblock*}{\textwidth}(1cm,1cm) \begin{minipage}[t][2cm][t]{0.4\textwidth} The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. The height of this minipage is 2cm. \end{minipage} \end{textblock*} \end{document}

The framed box is only to show that there is a minipage with a height of 2cm, but this doesn’t count.