Question

Find the maximum number of diagonals that can be drawn in n-sides polygon. Also, find number of diagonals if
i. n=12 sides
ii. n=15 sides
iii. decagon

Answer 1

Maximum no. of diagonals for $a_n$

n-sided polygon is given by

$\frac{n(n-3)}{2}$

$1)$ If $n=2$

$\frac{12(12-3)}{2}=6\times 9=54$

$\left(2\right)$ If $n=15$

$\frac{15(15-3)}{2}=15\times 6=90$

$\left(3\right)$ for a decagon

$n=10$

$\frac{10(10-3)}{2}=35$.