Thread: Simple Q: Are the Sides of a pyramid always of equal length?

This is a simple question however I do not know the answer to it and it's curiosity that has me posting this.

*Are the sides of any pyramid, meeting the apex, the same length?

So that includes every pyramid out there. Now to save confusion:

I am not asking if every pyramid has equal sides of length as the obvious answer is no.

I am asking In one particular pyramid (which has a base of any shape) are it's sides (the one's meeting the apex) always going to be the same length?

So for example the sides in a square pyramid meeting the apex are the same length. Would this also be the case for a rectangular pyramid?

Thanks

Originally Posted by Astar

This is a simple question however I do not know the answer to it and it's curiosity that has me posting this.

*Are the sides of any pyramid, meeting the apex, the same length?

So that includes every pyramid out there. Now to save confusion:

I am not asking if every pyramid has equal sides of length as the obvious answer is no.

I am asking In one particular pyramid (which has a base of any shape) are it's sides (the one's meeting the apex) always going to be the same length?

So for example the sides in a square pyramid meeting the apex are the same length. Would this also be the case for a rectangular pyramid?

Thanks

1. It depends how you define a pyramid: It is a solid with at least 4 apices, bounded by plane areas. The base area can be of any shape (even a star like area is possible) and the surface area is composed by triangles.

2. I've sketched 3 pyramids with identical base areas where the apex is perpendicular
- to one vertex of the base area
- to the centroid of the base area
- to the midpoint of one side of the base area.

3. By simple trigonometry you'll see that the lengthes of the edges of the surface are not necessarily equal.