A polygon is an enclosed figure on a plane bounded by \(3\) or more straight sides.
For a polygon,
The number of diagonals of a polygon having \(n\) sides can be calculated by using the following formula.
\(\begin{aligned} &\space\text{Number of diagonals} \\\\&=\dfrac{n(n-3)}{2} \end{aligned}\)
The number of vertices for a polygon is \(9\).
Find:
(i) the number of sides
(ii) the number of diagonals
(i)
Noted that,
number of vertices \(=\) number of sides.
Thus, the number of sides is \(9\).
(ii)
Noted that \(n=9\).
\(\begin{aligned} &\space\text{Number of diagonals} \\\\&=\dfrac{n(n-3)}{2} \\\\&=\dfrac{9(9-3)}{2} \\\\&=27. \end{aligned}\)
Steps to draw a polygon.
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