It is trivial to modify the left and right margins in beamer.
But what about the top and bottom?
If possible, I would like to reduce a little bit that top margin, marked with the hand-drawn red arrow:
MWE:
\documentclass[t]{beamer}
\setbeamersize{text margin left=0.5em, text margin right=0.5em}
\setbeamertemplate{frametitle}{\color{black}\bfseries\insertframetitle\par\vskip-6pt\hrulefill}
\newcommand\FourQuad[4]{
\colorbox{yellow}{\begin{minipage}[b][.40\textheight][t]{.49\textwidth}#1\end{minipage}}\hfill
\begin{minipage}[b][.40\textheight][t]{.49\textwidth}#2\end{minipage}\\
\begin{minipage}[b][.40\textheight][t]{.49\textwidth}#3\end{minipage}\hfill
\begin{minipage}[b][.40\textheight][t]{.49\textwidth}#4\end{minipage}
}
\begin{document}
\begin{frame}
\frametitle{A frame divided in four quadrants}
\FourQuad%
{First quadrant contents and some more text text text text more text text text text more text text text text more text text text text more text text text text more text text text text more text text text text}%
{
\centering
\rule{3cm}{2cm}
A test figure.
}%
{\begin{align*}
a &= b \\
&= c \\
& = d.
\end{align*}}%
{Fourth quadrant contents and some more text text text text more text text text text more text text text text more text text text text more text text text text more text text text text more text text text text}
\end{frame}
\end{document}