You can use the tcolorbox
package to easily create your box (you can use the beamer
skin). Setting the desired width for the box (and the text width inside the box) is just a matter of setting the appropriate keys. A little example; since the original beamer
theme used was not specified in the question, I defined my own colors to emulate the original ones; adjust the settings according to your needs:
\documentclass{beamer}
\usepackage[many]{tcolorbox}
\definecolor{myblue}{RGB}{0,112,214}
\makeatletter
\newtcolorbox{tcbexample}[1][]{
skin=beamer,
enhanced,
title=#1,
width=\paperwidth,
left=\Gm@lmargin,
right=\Gm@rmargin,
enlarge left by=-\Gm@lmargin,
enlarge right by=-\Gm@rmargin,
arc=0pt,
outer arc=0pt,
colback=myblue,
boxrule=0pt,
colupper=white,
colbacktitle=myblue!40!black
}
\makeatother
\begin{document}
\begin{frame}
\begin{tcbexample}
Some test text.
\end{tcbexample}
\begin{tcbexample}[A box with title]
Some longer test text that will span more than a line to illustrate text wrapping.
\end{tcbexample}
\end{frame}
\end{document}
The result:

\documentclass{...}
, the required\usepackage
's,\begin{document}
, and\end{document}
. That may seem tedious to you, but think of the extra work it represents for TeX.SX users willing to give you a hand. Help them help you: remove that one hurdle between you and a solution to your problem.