Question

The number of diagonals in a regular polygon of $100$ sides is

• A. 4950
• B. 4850
• C. 4750
• D. 4650

Answer 1

Answer: (B)

The number of diagonals in a regular polygon of $n$ sides is given by the following formula ${}^n{C}_2-n$
$\therefore$ The number of diagonals in a regular polygon of 100 sides
$={}^{100}{C}_2-100=\frac{100\cdot 99}{2}-100$
$=\frac{9900-200}{2}=\frac{9700}{2}=4850$