# Need to help to shade and label squares cut from the corners of the rectangle

I have just started learning using how to plot graphs using the TikZ package. I am still in my first steps. I appreciate if anybody can help me with the following:

I wrote the following code (see below) where I want to plot a 10x15 rectangle and then I cut a square from each corner (the square cut is the same from each corner). I want to shade each square cut (I know there is a command called filldraw but I didn't know to use it to achieve what I want), and then I want to show the dimensions of the rectangle on the graph (length is 15 and width is 10). I also want to show on the graph that the length of the square cut is "x". The reason why I want to do that is because I want to include the plot to the following problem that I intend to assign to my students during my recitation next week:

Statement of the Problem: We plan to form a 10x15 inch piece of tin into a box (without a top) by cutting a square from each corner and folding up the sides.

How much should we cut from each corner so that the volume of the resulting box is as big as possible ?

Hint: Let " x" be the length of the square cut from each corner

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw (-6,0) -- (6,0);
\draw (6,0) -- (6,-6);
\draw (6,-6) -- (-6,-6);
\draw (-6,0) -- (-6,-6);
\draw (-6,-1.3) -- (6,-1.3);
\draw (6,-4.7) -- (-6,-4.7);
\draw (4.7,0) -- (4.7,-6);
\draw (-4.7,0) -- (-4.7,-6);
\end{tikzpicture}
\end{document}

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One possibility:

The code:

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[x=.5cm,y=0.5cm,>=latex]
\def\RWd{15}
\def\RHt{10}
\def\CutSide{30pt}
\draw
(0,0) rectangle (\RWd,\RHt);
\path[draw,fill=cyan]
(0,0) rectangle ++(\CutSide,\CutSide)
(\RWd,0) rectangle ++(-\CutSide,\CutSide)
(0,\RHt) rectangle ++(\CutSide,-\CutSide)
(\RWd,\RHt) rectangle ++(-\CutSide,-\CutSide);
\begin{scope}[|<->|,help lines,text=black]
\draw
([yshift=-13pt]0,0) -- node[fill=white] {$15$} ([yshift=-13pt]\RWd,0);
\draw
([xshift=-13pt]0,0) -- node[fill=white] {$10$} ([xshift=-13pt]0,\RHt);
\draw
([yshift=13pt]0,\RHt) -- node[fill=white] {$x$} ++(\CutSide,0);
\end{scope}
\end{tikzpicture}

\end{document}


Control the height and width of the rectangle using \RHt, \RWd, respectively and the side of the cut squares using \CutSide.

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Thanks a lot for your help! –  Pat_Ho Aug 2 '14 at 17:13

Just for typing exercise with PSTricks.

## Option 1

\documentclass[pstricks,border=12pt,12pt,dvipsnames]{standalone}
\usepackage{pgfmath}
\usepackage{pst-node}
\psset{unit=5mm,dimen=m,shortput=nab,arrows=|*-|*}

\begin{document}
\begin{pspicture}[showgrid=false](-2,-2)(15,12)
\psframe(15,10)
\pcline[offset=-1](0,0)(15,0)\ncput*{$15$}
\pcline[offset=-1](0,10)(0,0)\ncput*{$10$}
\pcline[offset=1](0,10)(2,10)\ncput*{$x$}
\foreach \Point/\Angle in {{0,0}/0,{0,10}/-90,{15,10}/-180,{15,0}/-270}{%
\rput{\Angle}(\Point){\psframe[fillstyle=solid,fillcolor=Gray!50](2,2)}}
\end{pspicture}
\end{document}


## Option 2

\documentclass[pstricks,border=0pt,12pt,dvipsnames]{standalone}
\usepackage{pgfmath}
\usepackage{pst-node}
\psset{unit=5mm,dimen=m,shortput=nab,arrows=|*-|*,arcangle=-30,linejoin=2}

\begin{document}
\begin{pspicture}[showgrid=false](-2,-2)(16,11)
\psframe(15,10)
\pcline[offset=-1](0,0)(15,0)\ncput*{$15$}
\pcline[offset=-1](0,10)(0,0)\ncput*{$10$}
\psset{arrows=-}
\foreach \Point/\Angle in {{0,0}/0,{0,10}/-90,{15,10}/-180,{15,0}/-270}{%
\rput{\Angle}(\Point){%
\psframe[fillstyle=solid,fillcolor=Gray!50](3,3)%
\pcarc[linestyle=dashed](3,0)(3,3)_{\rput{*0}{$x$}}%
\pcarc[linestyle=dashed](3,3)(0,3)_{\rput{*0}{$x$}}%
}}
\end{pspicture}
\end{document}


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