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Area: rectangle and square

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

How big is a surface? You count unit squares and find the formula for the rectangle and the square.
📄 Open worksheet (PDF, German)

The video

In the video small pink squares fill a rectangle. They are counted.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:21 The unit square
  3. 0:40 Counting squares
  4. 1:06 Calculating faster
  5. 1:26 The square
  6. 1:46 Careful, mistake!
  7. 2:07 Try it yourself

The most important points

The unit square

A square with side 1 cm is called the unit square (das Einheitsquadrat). Its area is 1 square centimetre: \(1\text{ cm}^2\). The area (der Flächeninhalt) \(A\) tells you: How many unit squares fit into the shape?

A unit square: 1 cm long and 1 cm wide.
A unit square: 1 cm long and 1 cm wide.

Rectangle and square

A rectangle with \(a = 5\) cm and \(b = 3\) cm: 3 rows with 5 squares each, \(3 \cdot 5 = 15\). Rectangle: \(A = a \cdot b\). Square: \(A = a \cdot a\).

3 rows with 5 unit squares each: 15\text{ cm}^2.
3 rows with 5 unit squares each: \(15\text{ cm}^2\).

Do not mix them up: the perimeter (der Umfang) is the edge (in cm), the area is inside (in \(\text{cm}^2\)).

Careful, mistake: 16 cm is the perimeter, not the area.
Careful, mistake: 16 cm is the perimeter, not the area.

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 1/4
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 area. a) rectangle \(a = 7\) cm, \(b = 3\) cm b) square \(a = 8\) cm c) rectangle \(a = 4\) cm, \(b = 2{,}5\) cm

Show solution

a) \(21\text{ cm}^2\) b) \(64\text{ cm}^2\) c) \(10\text{ cm}^2\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Flächeninhalt von Rechteck und Quadrat (Einheitsquadrat, Quadratzentimeter, A = a · b, Unterschied zum Umfang). 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.