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Hello there,
I am creating a cube model with the dimensions 6 x 6 x 6 in. The cube is made up of three congruent square pyramids. How would I find the dimensions for the square pyramids (the sides of the pyramid are not the same length, the 3 square pyramids are just congruent). I was wondering if you could please explain how to find the measures of the square pyramids.

I got 6 x 6 x 6 for the bottom face
6 x 6 x 8.49 for the front and left face--used the Pythagorean Theorem)  
6 x 6 x 10.39 for the back face--used 3D Distance formula, using coordinates (0,6,0) and (6,0,6)
6 x 8.49 x 10.39 for the right face--again used the 3D Distance formula

Something about the answers just seem "off" when I drew it on graph paper. I thank you for your help.

Hi Jo,

You have the right dimensions, but in the wrong places.  Consider the summit of one of the pyramids (say (0,0,6)).  There is an edge that goes straight down, measuring 6.  (From (0,0,6) to (0,0,0).)
There are two edges that travel along the outside of the cube, measuring 6√2. (From (0,0,6) to (0,6,0) and from (0,0,6) to (6,0,0).)
There is only one edge that travels inside the cube, measuring 6√3 (From (0,0,6) to (6,6,0).)

The importance is there is only one "longest" edge per pyramid, not two.

Hope this helps,


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Azeem Hussain


I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.


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