Although Sketchup calculates the true lengths of arcs it does not calculate the true area of faces where part or all of the perimeter is made up of arc(s). Instead it uses the straight segments that are used to depict the arcs.
Open the entity window. Add a circle. Select the face to see its area.
Now select the circle edge. Change the number if segments by a lot.
Now select the face again. The area has changed!!!
This is not technically a bug. It was just lazy design.
There are applications where exact true area are very important.
I’ve started to write a ruby script to do it correctly. It’s not that hard to do.
But it shoul be corrected in the product.