Pythagorean theorem in 3D | Geometry | 8th grade | Khan Academy | Summary and Q&A
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Pythagorean theorem in 3D | Geometry | 8th grade | Khan Academy
TL;DR
Calculate the length of a specific edge in a geometric figure consisting of a rectangular prism and a right pyramid.
Key Insights
- 🗯️ The figure consists of a rectangular prism and a right pyramid.
- 🇦🇪 The dimensions of the rectangular prism are 3 units tall, 4 units wide, and 4 units long.
- 🗯️ The height of the right pyramid is 1 unit.
- 🦔 The length of one of the edges of the pyramid can be found using the Pythagorean theorem.
- 😥 The rectangular prism helps determine the length of the edge by providing halfway points.
- 🗯️ The length of one side of the pyramid forms a right triangle with the height of 1 unit.
- 🦔 The Pythagorean theorem is applied twice to find the length of the edge.
Transcript
- [Voiceover] So we have an interesting shape right over here. The base is a rectangular prism. And the dimensions of that rectangular prism, it's three units I guess we could say tall, four units wide, and then four units long. And then on top of that, on top of that, we have what you could call a right pyramid, where the height of this right pyra... Read More
Questions & Answers
Q: What are the dimensions of the rectangular prism in the figure?
The rectangular prism is 3 units tall, 4 units wide, and 4 units long.
Q: What is the height of the right pyramid in the figure?
The height of the right pyramid is 1 unit.
Q: What is the goal of the problem?
The goal is to determine the length of one of the edges of the pyramid.
Q: Which theorem is used to solve the problem?
The Pythagorean theorem is used to find the length of the edge.
Summary & Key Takeaways
-
The figure has a rectangular prism with dimensions 3 units tall, 4 units wide, and 4 units long.
-
On top of the rectangular prism is a right pyramid with a height of 1 unit.
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The goal is to find the length of one of the edges of the pyramid.
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