Question

The number of rectangles that can be obtained by joining four of th e twelve vertices of a $12$ -sided regular polygon is

• A. 66
• B. 30
• C. 24
• D. 15

Answer 1

Answer: (D)

We have,
$12$-sided regular polygon the diagonal of rectangle are equal
$\therefore$ Diagonals of rectangle passes through the centre of $12$-sided regular polygon $=6$
$\therefore$ Number of rectangles ${=}^6{C}_2=\frac{6!}{2!4!}=15$