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Units of area

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

Room, football pitch, city: you measure areas in \(\text{m}^2\), ha and \(\text{km}^2\). The conversion number is 100.
📄 Open worksheet (PDF, German)

The video

In the video one square metre is divided into \(10 \cdot 10\) small squares.

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 The square metre
  3. 0:33 The staircase
  4. 0:54 Are and hectare
  5. 1:16 Careful, mistake!
  6. 1:36 Try it yourself

The most important points

The square metre

\(1\text{ m}^2 = 10\text{ dm} \cdot 10\text{ dm} = 100\text{ dm}^2\). The length is used twice, so it is 100 and not 10.

A square metre holds 10 · 10 = 100 square decimetres.
A square metre holds \(10 \cdot 10 = 100\) square decimetres.

The staircase with 100

\(\text{km}^2\) – ha – a – \(\text{m}^2\) – \(\text{dm}^2\) – \(\text{cm}^2\) – \(\text{mm}^2\): from step to step \(100 = 10^2\). More: series Flächen, unit 07.

The unit staircase for areas.
The unit staircase for areas.

Are and hectare

\(1\text{ a} = 100\text{ m}^2\) (\(10\text{ m} \cdot 10\text{ m}\)), \(1\text{ ha} = 10\,000\text{ m}^2\) (\(100\text{ m} \cdot 100\text{ m}\)). A football pitch has about \(0{,}7\text{ ha}\).

One are and one hectare (not to scale).
One are and one hectare (not to scale).

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

Try it yourself

Task

a) \(3\text{ dm}^2\) to \(\text{cm}^2\) b) \(2\text{ ha}\) to \(\text{m}^2\) c) \(500\text{ dm}^2\) to \(\text{m}^2\)

Show solution

a) \(300\text{ cm}^2\) b) \(20\,000\text{ m}^2\) c) \(5\text{ m}^2\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Flächeneinheiten umrechnen (mm², cm², dm², m², a, ha, km², Umrechnungszahl 100). 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.