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Area: triangle

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

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

The video

In the video a copy of the triangle 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. 0:15 Base and height
  3. 0:29 Doubling
  4. 0:52 The formula
  5. 1:13 Careful, mistake!
  6. 1:28 Try it yourself

The most important points

The height (die Höhe) \(h\) goes from the top corner perpendicular to the base \(g\).

Base g = 5 cm, height h = 3 cm.
Base \(g = 5\) cm, height \(h = 3\) cm.

We make a copy and turn it by \(180^\circ\). Together they are a parallelogram with the same base and the same height.

Triangle and copy make a parallelogram.
Triangle and copy make a parallelogram.

Triangle

The triangle is half of it: \(A = g \cdot h : 2\). Here: \(5 \cdot 3 : 2 = 7{,}5\text{ cm}^2\). Do not forget: \(: 2\)!

A = g · h : 2.
\(A = g \cdot h : 2\).

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

Try it yourself

Task

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

Show solution

a) \(12\text{ cm}^2\) b) \(10{,}5\text{ cm}^2\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Flächeninhalt des Dreiecks (Grundseite, Höhe, A = g · 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.