Drag the point between the red square and the purple square. Play with it a bit.
Lets define:
R = area of red square
B = area of blue square
P = area of purple square
a = the angle labelled
Drag it to where the purple square is largest. Convince yourself that B + R is less than P.
Drag it to where the purple square is smallest. Convince yourself that B + R is greater than P.
What about in between these two points? Do you agree that there must be a point at which B + R is exactly equal to P?
What would a graph of a against P look like? Is there a formula that links a and P?