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The perimeter

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

How long is the edge of a shape? You unroll the edge and add all sides.
📄 Open worksheet (PDF, German)

The video

In the video the four sides of a rectangle fold one after another onto a straight line.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:11 Unrolling the edge
  3. 0:42 The formula
  4. 1:00 Square and triangle
  5. 1:30 Careful, mistake!
  6. 1:50 Try it yourself

The most important points

The perimeter (der Umfang) \(u\) is the length of the edge, once all the way round. You add all sides.

The edge unrolled: 5 + 3 + 5 + 3 = 16 cm.
The edge unrolled: \(5 + 3 + 5 + 3 = 16\) cm.

Formulas

Rectangle: \(u = 2 \cdot a + 2 \cdot b\) · Square: \(u = 4 \cdot a\) · Triangle: \(u = a + b + c\). The perimeter is a length: unit cm or m.

Side a appears twice, side b too.
Side \(a\) appears twice, side \(b\) too.
Square: 4 · 4 = 16 cm. Triangle: 3 + 4 + 5 = 12 cm.
Square: \(4 \cdot 4 = 16\) cm. Triangle: \(3 + 4 + 5 = 12\) cm.

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
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The worksheet – Page 2
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The worksheet – Page 3
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

Calculate the perimeter. a) rectangle \(a = 7\) cm, \(b = 4\) cm b) square \(a = 6\) cm c) triangle with 5 cm, 5 cm, 6 cm

Show solution

a) \(22\) cm b) \(24\) cm c) \(16\) cm

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: der Umfang von Rechteck, Quadrat und Dreieck (u = 2 · a + 2 · b, u = 4 · a, alle Seiten addieren). 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.