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  4. A convex polygon has 44 diagonals. The polygon is

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Q. A convex polygon has 44 diagonals. The polygon is

Permutations and Combinations

Solution:

If number of sides is $n$, then
total number of diagonals of a convex polygon $={ }^{ n } C _2- n =44$ (given)
$\Rightarrow n ( n -1)-2 n =88 \Rightarrow n ^2-3 n -88=0 \Rightarrow ( n -11)( n +8)=0$
$\Rightarrow n =11 \Rightarrow $ undecagon