Ok this looks easy, but it isn't. To solve it, you need to obtain three independent equations containing x,y and z that can be solved to determine the areas of the regions.

A square has sides 6 cm long. Four quarter circles are inscribed in the square. Determine the areas of the three different kinds of regions that are formed.

Here's the picture:

So you need to make 3 equations with three unknown then solve. I happen to know two of them. They are:

4x + 4y + z = 36

This is because there are 4 "x" regions, 4 "y" regions, and 1 "z" region making up the square with area 6^2, aka 36.

2x+3y+z = 9pi

this is because there are 2 "x" regions, 3 "y" regions, and 1 "z" region making up a quarter circle with area (r^2 pi)/4 = (36pi)/4 = 9pi

What is the third equation? Its more difficult to find than the first two, I believe. Make sure your answer isn't just a combination of the first two, like 2x + y = 36 - 9pi

Thank you for all the help you can offer me.