The number of rectangles that can be obtained | vedclass

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(D) rectangle is formed by two diagonals of a regular polygon that intersect at the center.For a regular polygon with $n$ sides,where $n$ is even,the

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$15$

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(D) rectangle is formed by two diagonals of a regular polygon that intersect at the center.For a regular polygon with $n$ sides,where $n$ is even,the number of such rectangles is given by the number of pairs of diameters.Here,$n = 12$,so the number of diameters (diagonals passing through the center) is $\frac{n}{2} = \frac{12}{2} = 6$.Any two of these $6$ diameters form a rectangle.Therefore,the number of rectangles is $^6C_2 = \frac{6 	imes 5}{2 	imes 1} = 15$.

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

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