Question

What is the number of diagonals in a
(i) heptagon
(ii) octagon
(iii) polygon of $12$ sides?

Answer 1

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

(i) For a heptagon:

no. of sides, $n=7$

$=\frac{n(n-3)}{2}$
$=\frac{7(7-3)}{2}$
$=\frac{7\times 4}{2}$
$=14$
(ii) For an octagon: $n=8$
$=\frac{n(n-3)}{2}$

$=\frac{8(8-3)}{2}$
$=\frac{8\times 5}{2}=20$

(iii) For a $12-$sided polygon:
$n=12$
$=\frac{n(n-3)}{2}$
$=\frac{12(12-3)}{2}$
$=\frac{12\times 9}{2}$
$=54$