Greek pentagōnon names a figure with five angles. English keeps that numerical construction in pentagon. The famous building takes its name from the shape, rather than supplying the word’s original meaning.
This view explains the components. They are pieces of one construction, not consecutive borrowing stages.
Sources
- Merriam-Webster · pentagon
Formation of the word.
- Merriam-Webster · -gon
Meaning and history of this component.