What is the sum of all areas shaded in blue in the following figure? The areas are constructed as follows. Start with a unit square and inscribe a circle. The area between the circle and the square is the first area. In each subsequent step, inscribe a new square inside the previous circle and then inscribe another circle inside the new square. In each step shade the area between the circle and the square. The question is to find the sum of all such areas if the steps are repeated infinitely.

In the figure, if ABCD and EFGC are squares with areas R and S respectively. What is the area of the blue region?

If blue rectangle area is equal to the sum of 3 squares areas combined as in image, what is relation between a,b,c & d?

What is the ratio of the blue shaded area to the orange shaded area in the following image?

If in each square, the blue and red areas are equal then find out the ratio of radius between big and small circle?