A diagonal of a polyhedron is a line segment connecting two non-adjacent vertices. How many diagonals does a pentagonal prism have?

Guest Jan 20, 2020

#1**+1 **

I'm not entirely sure about this answer, but I'll try it.

As pentagons have 5 vertices, this means they can have four diagonals to the other side of the pentagonal prism. Each diagonal is independent of the four others, so the answer would just be 5*4 = 20.

Badada Jan 21, 2020

#2**+2 **

**A diagonal of a polyhedron is a line segment connecting two non-adjacent vertices. How many diagonals does a pentagonal prism have?**

I assume:

\(\dbinom{\text{vertices}}{2} - \text{edges} \quad | \quad \text{vertices}=10,\ \text{edges} = 15 \)

\(\begin{array}{|rcll|} \hline && \mathbf{\dbinom{\text{vertices}}{2} - \text{edges}} \quad | \quad \text{vertices}=10,\ \text{edges} = 15 \\\\ &=& \dbinom{\text{10}}{2} - 15 \\\\ &=& \dfrac{10}{2}*\dfrac{9}{1} - 15 \\\\ &=& 45 - 15 \\ &=& \mathbf{30} \\ \hline \end{array} \)

A pentagonal prism has **30 **diagonals.

heureka Jan 21, 2020