Is there an algebraic proof for this? I was trying to solve how this relationship was made. Thanks! Also, what is the proper name for this relationship?
2026-03-28 01:07:10.1774660030
Relationship of a section cut parallel to a base of a pyramid and its height proof
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Check out this article about similarity. The article only talks about 2D shapes, but the same concept applies here. An algebraic proof is not needed here. The pyramid which only consists of the top $x$ units is similar to the whole pyramid. The ratio of the lengths of each pyramid is $\dfrac{x}{h}$. Hence, the ratio of the area of the bottom section of each pyramid is $\dfrac{x^2}{h^2}$.
The name of this relationship is simply "similarity".