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## Geometry (all content)

### Course: Geometry (all content)>Unit 9

Lesson 2: Pythagorean theorem application

# Pythagorean theorem in 3D

Discover how to find the length of an edge in a 3D shape using the Pythagorean theorem! This fun math lesson explores right pyramids and rectangular prisms, guiding you through solving for unknown lengths by applying the theorem multiple times.

## Want to join the conversation?

• Could you use the 3D pythagorean theorem which is a^2 + b^2 + c^2 = d^2 to figure out the edge of a pyramid given the side lengths of the base and the vertical height.
• Yes, you could use it but i personally like typing `√ a^2 + b^2 + c^2 = d` so it is calculated at once.
• I am colorblind and can not tell what is going on. Is there another video that someone could suggest?
• Let L, W, and H represent the dimensions (length, width, and height) of a rectangular prism, let C represent a diagonal of the bottom face, and let D represent a long diagonal of the prism.

We use the regular (2-dimensional) Pythagorean theorem on two right triangles.

One right triangle has legs L & W and hypotenuse C. This gives L^2+W^2=C^2.

The other right triangle has legs C & H and hypotenuse D. This gives C^2+H^2=D^2.

Substituting the first equation into the second equation gives the 3-dimensional result L^2+W^2+H^2=D^2. Notice how this is just like the 2-dimensional Pythagorean theorem, except that one more square is being added.
• Can you make more another video to help explain the Harder Pythagorean theorem in 3D problems?
• I find the whole video confusing. I would have preferred that he used a cube. When I looked up this video I thought it would thoroughly explain how to solve Pythagoras' theorem questions involving cubes but he seems to be using some sort of pyramid and it is all so confusing. I searched this to clarify this- http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/pythagoras3drev1.shtml

But I'm still as confused as I was after looking at that website
• why do we need the other dimensions then like the 3?
• I think what he meant was basically the 3 in the problem was useless. And yes, it is useless. Sometimes you're given a problem with information you won't need. You just left that out to the side.
• 2006 was 1 year after I was born! Did you know that?!
• no :0 but now i do thanks
• There is too much going on here for my mush of a brain to understand :(
• fr same
• At I don’t quite understand how Sal knows it’s a 90 degree angle
• It's a 90 degree angle because if you just look at the rectangle based pyramid, the height is straight, which means that any line across the rectangle based would make it into a right angle.
• why is the hypotenuse the a^2 and not c?
(i mean in Pythagorean theorem that's the formula that comes out right?(a^2+b^2=c^2))