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The prism

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

A prism has two equal bases and a lateral surface made of rectangles. You learn volume and surface area.
📄 Open worksheet (PDF, German)

The video

In the video a prism is cut into slices like a loaf of bread. Then it is unfolded into a net.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:18 What is a prism?
  3. 0:53 The volume
  4. 1:44 The net
  5. 2:21 The surface area
  6. 2:44 Careful, mistake!
  7. 3:02 Try it yourself

The most important points

The prism

The base (die Grundfläche) and the top face (die Deckfläche) are equal and parallel. The side faces are rectangles; together they are the lateral surface (der Mantel). The distance between base and top face is the height \(h\).

Triangular prism: base at the front, lateral surface orange, h = 4 cm.
Triangular prism: base at the front, lateral surface orange, \(h = 4\) cm.

The volume

\(V = G \cdot h\). Here: \(G = 4 \cdot 3 : 2 = 6\text{ cm}^2\), \(V = 6 \cdot 4 = 24\text{ cm}^3\).

Four slices, each 6\text{ cm}^3.
Four slices, each \(6\text{ cm}^3\).

The surface area

The lateral surface is a rectangle: \(M = u \cdot h = 12 \cdot 4 = 48\text{ cm}^2\). \(O = 2 \cdot G + M = 12 + 48 = 60\text{ cm}^2\).

The net: two triangles and the lateral surface.
The net: two triangles and the lateral surface.

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

A prism has \(G = 8\text{ cm}^2\), \(u = 12\) cm and \(h = 5\) cm. Calculate \(V\) and \(O\).

Show solution

\(V = 40\text{ cm}^3\), \(M = 60\text{ cm}^2\), \(O = 16 + 60 = 76\text{ cm}^2\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Prisma (Grundfläche, Mantel, Höhe, V = G · h, M = u · h, O = 2 · G + M). 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.