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

Jan 20, 2020

#1
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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.

Jan 21, 2020
#2
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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.

Jan 21, 2020