In the given diagram, some diagonals of a regular decagon are intersecting such that they form another small decagon inside the original decagon. If each side of the larger decagon be $2 \mathrm{cm},$ find the side of the smaller decagon.

In the following figure of regular dodecagon find the area of all the four kites, where each of the four kites has two unequal diagonals and the side of each square, each triangle and each kite is $1 \mathrm{cm}.$

If each side of a regular dodecagon is $1 \mathrm{cm},$ find the second longest diagonal of the dodecagon.