Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to extend a triangular area into a prism.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Triangle area and multiplication.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A triangular prism has a right-triangle cross-section with legs 6 cm and 8 cm and a perpendicular length of 10 cm. Find its volume.
Why this math matters
A prism's volume equals its constant cross-sectional area multiplied by its perpendicular length. Identify a constant cross-section before using the prism formula for a three-dimensional object.
Set up the model
A useful answer starts with clear assumptions:
- The triangular cross-section stays constant along the prism.
- The 10 cm length is perpendicular to the triangular face.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Extend a triangular area into a prism
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A triangular prism has a right-triangle cross-section with legs 6 cm and 8 cm and a perpendicular length of 10 cm. Find its volume.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
cross-sectional area = (1/2)(6)(8) = 24 cm²
The perpendicular legs act as the triangle's base and height.
Apply the relationship
V = cross-sectional area × length = 24 × 10
The prism can be viewed as equal triangular layers extending through the length.
Check and interpret
V = 240 cm³
An area multiplied by a length yields cubic units.
The result
V = 240 cm³
An area multiplied by a length yields cubic units.
Common mistakes to catch
- Multiplying all three listed lengths without halving treats the triangular face as a rectangle.
- The prism length and the triangle height describe different directions.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
A prism's cross-section has area 15 m² and its perpendicular length is 4 m. Find its volume.
Show a hint
Use V = Bh.
Reveal answer and explanation
60 m³
15 × 4 = 60.
Practice 2
A triangular prism has volume 120 cm³ and length 8 cm. Its triangular base is 5 cm wide. Find that triangle's perpendicular height.
Show a hint
First recover cross-sectional area, then use triangle area.
Reveal answer and explanation
6 cm
The area is 120/8 = 15 cm². Solving (1/2)(5)h = 15 gives h = 6.
Take the idea with you
Identify a constant cross-section before using the prism formula for a three-dimensional object.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Count all faces in a rectangular box
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