Question

Verify Euler’s formula for pentagonal pyramid and square prism.

Answer 1

Pentagonal Pyramid

Number of faces $\left(F\right)=7$

Number of edges $\left(E\right)=15$

Number of vertices $\left(V\right)=10$

$F+V=7+10=17$

$E+2=15+2=17$

$F+V=E+2$

Euler’s formula is verified.

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Square prism

Number of faces $\left(F\right)=5$

Number of edges $\left(E\right)=8$

Number of vertices $\left(V\right)=5$

$$\begin{gathered} F+V=5+5=10 \\ E+2=8+2=10 \\ F+V=E+2 \end{gathered}$$

Hence, Euler’s formula is verified.