Wie es mir scheint ist die Aufgabe doch etwas zu kniffelig formuliert.
Ich werde sie auflösen, bevor sich Jemand damit stundenlang beschäftigt...
Arbeitsfläche:$$\mathrm{\ }$$
1.920 Pixel x 1.080 Pixel = 2.073.600 Pixel = 2,073.6 Megapixel
Sichtbare Fläche:
$$\underset{\,\,\,\,{\textcolor[rgb]{0.66,0.66,0.66}{\rightarrow {\mathtt{breite, hoehe}}}}}{{solve}}{\left(\begin{array}{l}{{\mathtt{breite}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{hoehe}}}^{{\mathtt{2}}}={\left({\mathtt{32}}{\mathtt{\,\times\,}}{\mathtt{2.54}}\right)}^{{\mathtt{2}}}\\
{\frac{{\mathtt{breite}}}{{\mathtt{hoehe}}}}={\frac{{\mathtt{1\,920}}}{{\mathtt{1\,080}}}}\end{array}\right)} \Rightarrow \left\{ \begin{array}{l}{\mathtt{breite}} = {\mathtt{\,-\,}}{\frac{{\mathtt{32\,512}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{337}}}}\right)}}\\
{\mathtt{hoehe}} = {\mathtt{\,-\,}}{\frac{{\mathtt{18\,288}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{337}}}}\right)}}\\
{\mathtt{breite}} = {\frac{{\mathtt{32\,512}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{337}}}}\right)}}\\
{\mathtt{hoehe}} = {\frac{{\mathtt{18\,288}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{337}}}}\right)}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{breite}} = -{\mathtt{70.841\: \!659\: \!657\: \!483\: \!365\: \!8}}\\
{\mathtt{hoehe}} = -{\mathtt{39.848\: \!433\: \!557\: \!334\: \!393\: \!3}}\\
{\mathtt{breite}} = {\mathtt{70.841\: \!659\: \!657\: \!483\: \!365\: \!8}}\\
{\mathtt{hoehe}} = {\mathtt{39.848\: \!433\: \!557\: \!334\: \!393\: \!3}}\\
\end{array} \right\}$$
Die negativen Längen ignoriere ich einfach:
$${\mathtt{flaeche}} = \left({\frac{{\mathtt{32\,512}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{337}}}}\right)}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{18\,288}}}{\left({\mathtt{25}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{337}}}}\right)}}\right) \Rightarrow {\mathtt{flaeche}} = {\mathtt{2\,822.929\: \!167\: \!952\: \!522\: \!255\: \!2}}$$cm²
!
(y)
