The neverending circle-square construction

Author:
Judith12
Topic:
Circle, Square
In this construction, we are starting off with a circle that has a radius of 10 cm. Then we draw a square in the circle, then a circle in the square and so on. Have a look at the construction.
Now your task is to figure out the total area of all the circles. If you get stuck use the hints. Now can you do the same for the squares without any help?