Consider regular polygons with number of sides n=3,4,5.....as shown in the figure. The center of mass of all the polygons is at height h from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is $$\triangle$$. Then $$\triangle$$ depends on n and has

A

$$\triangle=h \sin^{2}(\frac{\pi}{n})$$

B

$$\triangle=h (\frac{1}{\cos(\frac{\pi}{n})}-1)$$

C

$$\triangle=h \sin(\frac{2\pi}{n})$$

D

$$\triangle=h \tan^{2}(\frac{\pi}{2n})$$