A square based pyramid has $5$ faces and $5$ vertices. Find the number of edges.

6

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8

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10

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12

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Solution

The correct option is B $8$
Euler's polyhedron formula, $V - E + F = 2$
$V$ $=$ number of vertices $=$ $5$
$E$ $=$ number of edges $= ?$
$F$ $=$ number of faces $=$ $5$
Thus $5 - E + 5 = 2$
$\Rightarrow E = 10 - 2$
$\Rightarrow E = 8$
Number of edges $=$ $8$

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