• LÖSUNG: Flächeninhalt von Figuren (2)
  • MNWeG
  • 14.01.2022
  • Mathematik
  • Messen
  • E (Expertenstandard)
  • 6
  • Arbeitsblatt
Um die Lizenzinformationen zu sehen, klicken Sie bitte den gewünschten Inhalt an.
1
Hier wird EIN möglicher Lösungsweg gezeigt.
Dein Lösungsweg kann sich hiervon unterscheiden (z.B. wenn du die Teilflächen anders eingeteilt hast). Solange aber das Ergebnis stimmt, hast du alles richtig gemacht!
Bist du mit deinem Rechenweg unsicher, dann frage einen Experten.
ABCDEFGHIJKLMNOPQRSTUVWXYZ

A1\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{1}

A2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{2}

A3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{3}

A5\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{5}

A4\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{4}

A6\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{6}

A9\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{9}

A11\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{11}

A8\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{8}

A7\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{7}

A10\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{10}

A12\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{12}

Aufgabe 1

Schritt 1: Figur in sinnvolle Teilflächen unterteilen und benennen (siehe vorherige Seite).



Schritt 2: Teilflächen berechnen.

A2=12aha=123cm1cm=123cm2=1,5cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{2}&=\frac{1}{2}\cdot a \cdot h_{a}\\ &=\frac{1}{2}\cdot 3cm \cdot 1cm\\ &=\frac{1}{2}\cdot 3cm²\\ &={\underline{\underline{1{,}5cm²}}} \end{aligned}
A1=ab=4cm1cm=4cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{1}&=a \cdot b\\ &=4cm \cdot 1cm\\ &={\underline{\underline{4cm²}}} \end{aligned}
A1=ab=15cm2cm=30cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{1}&=a \cdot b\\ &=15cm \cdot 2cm\\ &={\underline{\underline{30cm²}}} \end{aligned}
A4=ab=5cm3cm=15cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{4}&=a \cdot b\\ &=5cm \cdot 3cm\\ &={\underline{\underline{15cm²}}} \end{aligned}
A5=aha=5cm3cm=15cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{5}&=a \cdot h_{a}\\ &=5cm \cdot 3cm\\ &={\underline{\underline{15cm²}}} \end{aligned}
A6=ab=3cm2cm=6cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{6}&=a \cdot b\\ &=3cm \cdot 2cm\\ &={\underline{\underline{6cm²}}} \end{aligned}
A7=aha=6cm3cm=18cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{7}&=a \cdot h_{a}\\ &=6cm \cdot 3cm\\ &={\underline{\underline{18cm²}}} \end{aligned}
A8=ab=3cm11cm=33cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{8}&=a \cdot b\\ &=3cm \cdot 11cm\\ &={\underline{\underline{33cm²}}} \end{aligned}
A9=12aha=129cm5cm=1245cm2=22,5cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{9}&=\frac{1}{2}\cdot a \cdot h_{a}\\ &=\frac{1}{2}\cdot 9cm \cdot 5cm\\ &=\frac{1}{2}\cdot 45cm²\\ &={\underline{\underline{22{,}5cm²}}} \end{aligned}
A11=(a+c)ha2=(5cm+1cm)2cm2=(6cm)2cm2=12cm22=6cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{11}&=\frac{(a+c) \cdot h_{a}}{2}\\ &=\frac{(5cm+1cm) \cdot 2cm}{2}\\ &=\frac{(6cm) \cdot 2cm}{2}\\ &=\frac{12cm² }{2}\\ &={\underline{\underline{6cm²}}} \end{aligned}
A12=12aha=121cm5cm=125cm2=2,5cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{12}&=\frac{1}{2}\cdot a \cdot h_{a}\\ &=\frac{1}{2}\cdot 1cm \cdot 5cm\\ &=\frac{1}{2}\cdot 5cm²\\ &={\underline{\underline{2{,}5cm²}}} \end{aligned}
A10=ab=8cm5cm=40cm2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{10}&=a \cdot b\\ &=8cm \cdot 5cm\\ &={\underline{\underline{40cm²}}} \end{aligned}

Schritt 3: Teilflächen addieren.

Agesamt=A1+A2+A3+A4+A5+A6+A7+A8+A9+A10+A11+A12=4cm2+1,5cm2+30cm2+15cm2+15cm2+6cm2+18cm2+33cm2+22,5cm2    +40cm2+6cm2+2,5cm2=193,5cm²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{gesamt}&=A_{1}+A_{2}+A_{3}+A_{4}+A_{5}+A_{6}+A_{7}+A_{8}+A_{9}+A_{10}+A_{11}+A_{12}\\ &=4cm²+1{,}5cm²+30cm²+15cm²+15cm²+6cm²+18cm²+33cm²+22{,}5cm²\\ &\ \ \ \ +40cm²+6cm²+2{,}5cm^2\\ &=\textbf{\underline{\underline{193{,}5cm²}}} \end{aligned}
x