Scaling issues with Tikz

Question

I have two Tikz block code one after the other in my document in an enumerated list, Why does the following code scale the two Tikz figure differently? I am using the tkz-euclide package.

\documentclass{article}
\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{backgrounds}
\usetikzlibrary{shapes.geometric}
\usepackage{tkz-euclide}
\usetkzobj{all}


\begin{document}

Find the area of the triangle:
\vspace{-1em}
\begin{center}
\resizebox{2.5in}{!}{
\begin{tikzpicture}
\coordinate (Q) at (0,0);
\coordinate (A) at ($(Q)+(40:5)$);
\coordinate (P) at ($(Q)+(150:4)$);
\draw (A) -- (Q) -- (P) -- cycle;
\tkzLabelPoint[below](Q){$Q$};
\tkzLabelPoint[right](A){$A$};
\tkzLabelPoint[left](P){$P$};
\path (A) -- node [midway,above] {$11$} (P);
\path (A) -- node [midway,below right] {$9$} (Q);
\path (P) -- node [midway,below left] {6} (Q);
\end{tikzpicture}}
\end{center}

The diagram below is the plan of a field. Find the area of the field.
\vspace{-1em}
\begin{center}
\resizebox{2.5in}{!}{
\begin{tikzpicture}
\coordinate (P) at (0,0);
\coordinate (S) at ($(P)+(-20:2)$);
\coordinate (Q) at ($(P)+(110:2)$);
\coordinate (R) at ($(P)+(45:2.5)$);
\draw (P) -- (Q) -- (R) -- (S) -- cycle;
\draw[dashed] (P) -- (R);
\tkzLabelPoint[left](Q){$Q$};
\tkzLabelPoint[left](P){$P$};
\tkzLabelPoint[right](S){$S$};
\tkzLabelPoint[right](R){$R$};
\path (P) -- node [midway,sloped,above] {$650$} (R);

\tkzLabelAngle[pos = 0.35](P,Q,R){$56^\circ$};
\tkzMarkAngle[size=0.65cm,](P,Q,R);
\tkzLabelAngle[pos = 0.35](S,P,R){$44^\circ$};
\tkzMarkAngle[size=0.65cm,](S,P,R);
\tkzLabelAngle[pos = 0.35](R,P,Q){$83^\circ$};
\tkzMarkAngle[size=0.65cm,](R,P,Q);
\tkzLabelAngle[pos = 0.35](P,R,S){$65^\circ$};
\tkzMarkAngle[size=0.65cm,](P,R,S);
\end{tikzpicture}}
\end{center}

\end{document}

Answer 1

That's because your original drawings (before scaling) were one much bigger and one much smaller than your desired size. You should try something like the scale option or the x=legth,y=length, which does not mess with the text.

(p.s. i'm not familiar with tkzMarkAngle but it sounds somehow wrong to specify size in cm instead of the figure units)

  \documentclass{article}
  \usepackage{pgfplots}
  \usepackage{tikz}
  \usetikzlibrary{calc}
  \usetikzlibrary{backgrounds}
  \usetikzlibrary{shapes.geometric}
  \usepackage{tkz-euclide}
  \usetkzobj{all}


  \begin{document}

    Find the area of the triangle:
    \vspace{-1em}
    \begin{center}
      %\resizebox{2.5in}{!}{
        \begin{tikzpicture}[scale=0.8]
          \coordinate (Q) at (0,0);
          \coordinate (A) at ($(Q)+(40:5)$);
          \coordinate (P) at ($(Q)+(150:4)$);
          \draw (A) -- (Q) -- (P) -- cycle;
          \tkzLabelPoint[below](Q){$Q$};
          \tkzLabelPoint[right](A){$A$};
          \tkzLabelPoint[left](P){$P$};
          \path (A) -- node [midway,above] {$11$} (P);
          \path (A) -- node [midway,below right] {$9$} (Q);
          \path (P) -- node [midway,below left] {6} (Q);
        \end{tikzpicture}%}
    \end{center}

    The diagram below is the plan of a field. Find the area of the field.
    \vspace{-1em}
    \begin{center}
      %\resizebox{2.5in}{!}{
        \begin{tikzpicture}[scale=1.8]
          \coordinate (P) at (0,0);
          \coordinate (S) at ($(P)+(-20:2)$);
          \coordinate (Q) at ($(P)+(110:2)$);
          \coordinate (R) at ($(P)+(45:2.5)$);
          \draw (P) -- (Q) -- (R) -- (S) -- cycle;
          \draw[dashed] (P) -- (R);
          \tkzLabelPoint[left](Q){$Q$};
          \tkzLabelPoint[left](P){$P$};
          \tkzLabelPoint[right](S){$S$};
          \tkzLabelPoint[right](R){$R$};
          \path (P) -- node [midway,sloped,above] {$650$} (R);

          \tkzLabelAngle[pos = 0.35](P,Q,R){$56^\circ$};
          %\tkzMarkAngle[size=0.65cm,](P,Q,R);
          \tkzMarkAngle[size=0.65](P,Q,R);
          \tkzLabelAngle[pos = 0.35](S,P,R){$44^\circ$};
          %\tkzMarkAngle[size=0.65cm,](S,P,R);
          \tkzMarkAngle[size=0.65](S,P,R);
          \tkzLabelAngle[pos = 0.35](R,P,Q){$83^\circ$};
          %\tkzMarkAngle[size=0.65cm,](R,P,Q);
          \tkzMarkAngle[size=0.65](R,P,Q);
          \tkzLabelAngle[pos = 0.35](P,R,S){$65^\circ$};
          %\tkzMarkAngle[size=0.65cm,](P,R,S);
          \tkzMarkAngle[size=0.65](P,R,S);
        \end{tikzpicture}%}
    \end{center}

  \end{document}

Answer 2

Firstly \resizeboxis a bad idea because you scale all objects (points, lines and fonts). Davide answer is correct you need to use scale optionfrom tikZ.

I put my code because tkz-euclide has a special syntax without ; and some commands can be simplify. You don't need to load Tikzbecause pgfplots and Tkz-Euclide use TikZ If the big part of your code use TikZwhy use tkz-euclide. It's a lot of code useless. Then when you use tkz-euclide, TikZ is always behind so when you don't know how do something you can can use Tikz but It's preferable to avoid the mixing. I use mark=none because angles are not equal.

I compile the code with the new version of tkz-euclide is here

 \documentclass{article}
  \usepackage{tkz-euclide}

\begin{document}

  Find the area of the triangle:

\begin{tikzpicture}[x=.8cm,y=.8cm]
  \tkzDefPoint(0,0){Q}
  \tkzDefShiftPoint[Q](40:5){A}  
  \tkzDefShiftPoint[Q](150:4){P} 
    \tkzDrawPolygon(A,P,Q)
  \tkzLabelPoint[below](Q){$Q$}
  \tkzLabelPoint[right](A){$A$}
  \tkzLabelPoint[left](P){$P$}
    \tkzLabelSegment[swap](A,P){$11$}
    \tkzLabelSegment[](A,Q){$9$}
    \tkzLabelSegment[](Q,P){$6$}
\end{tikzpicture}

 The diagram below is the plan of a field. Find the area of the field.

\begin{tikzpicture}[scale=1.8]
  \tkzDefPoint(0,0){P}
  \tkzDefShiftPoint[P](-20:2){S}  
  \tkzDefShiftPoint[P](110:2){Q} 
    \tkzDefShiftPoint[P](45:2.5){R} 
    \tkzDrawPolygon(P,...,S)
  \tkzDrawSegment[dashed](P,R)
  \tkzLabelPoint[left](Q){$Q$}
  \tkzLabelPoint[left](P){$P$}
  \tkzLabelPoint[right](S){$S$}
  \tkzLabelPoint[right](R){$R$}
  \tkzLabelSegment[sloped](P,R){$650$}
  \tkzLabelAngle[pos = 0.35](P,Q,R){$56^\circ$}
  \tkzLabelAngle[pos = 0.35](S,P,R){$44^\circ$}
  \tkzLabelAngle[pos = 0.35](R,P,Q){$83^\circ$}
  \tkzLabelAngle[pos = 0.35](P,R,S){$65^\circ$}
  \tkzMarkAngles[mark=none,size=0.65](P,R,S R,P,Q S,P,R P,Q,R)
\end{tikzpicture}

\end{document}