Square Quadrants

The areas of the regions illustrated above can be found from the equations

(1)

(2)

Since we want to solve for three variables, we need a third equation. This can be taken as

(3)

where

(4)

(5)

leading to

(6)

Combining the equations (1), (2), and (6) gives the matrix equation

(7)

which can be inverted to yield

			(8)
			(9)
			(10)