>>10950764(Fucked up the formating in previous response so here goes again.)
Ok I actually found a mistake in my solution and think I got it now. I will try writing my solution down.
First calculate h from the yellow triangle (see figure):
Now the lower part of my figure. To obtain the green area in the lower image we simply integrate along the outline of the circle (by using the red triangle to obtain an equation for ) from to and then subtract the grey area (which is given as ). The area which we are supposed to find is then simply 4 times that.
Substitution
leads to:
Then you can use to express it in terms of the other area.