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Composite shapes

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

There is no formula for an L-shape. You split it up or you complete it.
📄 Open worksheet (PDF, German)

The video

In the video an L-shape is split up and completed. Both ways give the same result.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:19 Splitting up
  3. 0:42 Completing
  4. 1:12 Rectangle and triangle
  5. 1:38 Careful, mistake!
  6. 2:02 Try it yourself

The most important points

Splitting up (zerlegen)

Cut the shape into parts you know and add: \(6 \cdot 2 + 4 \cdot 2 = 20\text{ cm}^2\).

Two rectangles: 12 + 8 = 20\text{ cm}^2.
Two rectangles: \(12 + 8 = 20\text{ cm}^2\).

Completing (ergänzen)

Complete to a big shape and subtract what is too much: \(6 \cdot 4 - 2 \cdot 2 = 20\text{ cm}^2\).

Big rectangle minus the missing piece.
Big rectangle minus the missing piece.

When splitting up, nothing may overlap: every piece counts exactly once.

House: rectangle 12\text{ cm}^2 plus triangle 4\text{ cm}^2.
House: rectangle \(12\text{ cm}^2\) plus triangle \(4\text{ cm}^2\).

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
Page 1/3
The worksheet – Page 2
Page 2/3
Show the worksheet solutions
The worksheet – Page 3
Page 3/3

Try it yourself

Task

An L-shape is 10 m long and 8 m wide on the outside. A piece 4 m × 3 m is missing at one corner. How big is the area?

Show solution

\(80 - 12 = 68\text{ m}^2\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Flächeninhalt zusammengesetzter Figuren (zerlegen und ergänzen, Rechtecke und Dreiecke). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.