How to find dimensions of a shape layer
Assuming an irregular shape, here's a manual method to do it.

Create a solid layer of any color, stacked above the shape layer. Change its opacity to around 30%, enough to see the shape layer underneath. Unlink the scale controllers (X and Y) so that they can be scaled independently. Move and rescale the solid so that it can serve as a bounding box for the shape layer. Your original solid size should have been the same as your comp size, so the dimensions of your shape layer are

Shape width = Composition width * 'X' scale % of solid layer
Shape height = Composition height * 'Y' scale % of solid layer


Of course, this is a crude method for one-time polling. There's probably an expression for dynamically updated values if the shape is animated.