How can i compute perimeter and area of a skeletonized circle?
It is not clear if the skeletonized image can be reversed to a contour image. Skeletonization is often done by calculating the distance transform and then thresholding the result or performing a non-maximum suppression. At this point you have already lost too much information and the features, you are asking for cannot be calculated.

If you have the distance transform, you can approximate those values:


You get the radius ($r$) of the circle from the height of peak which represents the circle (the skeleton of an ideal circle would be a dot)
Perimeter = $2\pi r$
Area = $\pi r^2$
Convex hull $\rightarrow$ draw a circle with radius $r$ at the position where the peak is