• Fläche berechnen
  • MNWeG
  • 14.01.2022
  • Mathematik
  • Messen
  • R (Regelstandard)
  • 6
  • Arbeitsblatt
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Hinweis

Du brauchst für die Bearbeitung dieses Materials die korrekten Ergebnisse des Materials AB: Höhen zeichnen!
Kontrolliere also unbedingt zuerst, ob du dort alles richtig gemacht hast!

1
Berechne den Flächeninhalt (A\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} A_\vartriangle) der Dreiecke im 4-Schritt-Löseverfahren und überprüfe deine Ergebnisse anhand der Angaben in der Tabelle.
Wenn sich dein Ergebnis um ±0,5cm²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} ±0{,}5cm² unterscheidet, dann liegt dies noch in der Messtoleranz und gilt als richtig!

Beispiel:

AD=aha2=3,6cm2,4cm2=8,64cm²2=4,32cm²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} A_{D}&=\frac{a \cdot h_{a}}{2}\\ &=\frac{3{,}6cm \cdot 2{,}4cm}{2}\\ &=\frac{8{,}64cm²}{2}\\ &=\textbf{\underline{\underline{4{,}32cm²}}} \end{aligned}

Grundseite a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} a = 3,6cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 3{,}6cm
Höhe von a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} a = 2,4cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 2{,}4cm

Aufgabe

Grundseite

Höhe

Ergebnis

Beispiel

a=3,6cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} a=3{,}6cm

ha=2,4cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} h_{a}=2{,}4cm

AD=4,32cm²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{D}=4{,}32cm²

1

c=7,8cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} c=7{,}8cm

hc=4,5cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} h_{c}=4{,}5cm

AD=17,55cm²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{D}=17{,}55cm²

2

c=11,7cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} c=11{,}7cm

hc=3cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} h_{c}=3cm

AD=17,55cm²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{D}=17{,}55cm²

3

b=5,1cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} b=5{,}1cm

hb=5,5cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} h_{b}=5{,}5cm

AD=14,025cm²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{D}=14{,}025cm²

4

c=10,4cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} c=10{,}4cm

hc=3,9cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} h_{c}=3{,}9cm

AD=20,28cm²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{D}=20{,}28cm²

5

b=8,1cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} b=8{,}1cm

hb=5,9cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} h_{b}=5{,}9cm

AD=23,895cm²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{D}=23{,}895cm²

6

a=8,1cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} a=8{,}1cm

ha=5,2cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} h_{a}=5{,}2cm

AD=21,06cm²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{D}=21{,}06cm²

7

b=15cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} b=15cm

hb=2,7cm\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} h_{b}=2{,}7cm

AD=20,25cm²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} A_{D}=20{,}25cm²