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)

4850

Answer 2

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
$={ }^{100} C_{2}-100=\frac{100 \cdot 99}{2}-100$
$=\frac{9900-200}{2} =\frac{9700}{2}=4850$