What is the number of diagonals in a

Question:

What is the number of diagonals in a

(i) heptagon

(ii) octagon

(iii) polygon of 12 sides?

Solution:

Number of diagonal in an $\mathrm{n}$-sided polygon $=\frac{n(n-3)}{2}$

(i) For a heptagon:

$n=7 \Rightarrow \frac{n(n-3)}{2}=\frac{7(7-3)}{2}=\frac{28}{2}=14$

(ii) For an octagon:

$n=8 \Rightarrow \frac{n(n-3)}{2}=\frac{8(8-3)}{2}=\frac{40}{2}=20$

(iii) For a 12-sided polygon:

$n=12 \Rightarrow \frac{n(n-3)}{2}=\frac{12(12-3)}{2}=\frac{108}{2}=54$

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