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Area: trapezium

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

Two equal trapeziums make a parallelogram. This is how you find the formula for the trapezium.
📄 Open worksheet (PDF, German)

The video

In the video a copy of the trapezium is turned by half a turn.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:12 The sides and the height
  3. 0:30 Doubling
  4. 0:58 The formula
  5. 1:14 Careful, mistake!
  6. 1:37 Try it yourself

The most important points

A trapezium (das Trapez) has two parallel sides \(a\) and \(c\). The height \(h\) is their distance.

a = 6 cm, c = 2 cm, h = 3 cm.
\(a = 6\) cm, \(c = 2\) cm, \(h = 3\) cm.

Trapezium and copy make a parallelogram. Its base is \(a + c\).

The base of the parallelogram is a + c = 8 cm.
The base of the parallelogram is \(a + c = 8\) cm.

Trapezium

\(A = (a + c) \cdot h : 2\). Here: \((6 + 2) \cdot 3 : 2 = 12\text{ cm}^2\). The bracket is important: first \(a + c\)!

A = (a + c) · h : 2.
\(A = (a + c) \cdot h : 2\).

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 1/4
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

Calculate the area. a) \(a = 7\) cm, \(c = 3\) cm, \(h = 4\) cm b) \(a = 10\) cm, \(c = 6\) cm, \(h = 5\) cm

Show solution

a) \(20\text{ cm}^2\) b) \(40\text{ cm}^2\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Flächeninhalt des Trapezes (parallele Seiten a und c, Höhe, A = (a + c) · h : 2). 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.