1. The problem statement, all variables and given/known data I am after finding general geometric expressions for a quarter-circular spandrel that is split into two segments along either its domain or range (they are equal). I.e. Taking the geometry provided in the sketch below (Figure 1) I am after expressions for area and centroids x1, y1 and x2, y2 (Figure 2). http://oi47.tinypic.com/95y4ig.jpg Figure 1 http://oi46.tinypic.com/35i3pc7.jpg Figure 2 2. Relevant equations Area of circle = ∏r2 Equation of quarter circle: y(x) = √(x2-r2) 3. The attempt at a solution I can define the area under the quarter circle by some simple geometry, chiefly: Area of rectangle = r2 Area of quarter circle = ∏r2/4 Subtracting the two leaves me with the area of the spandrel: A = r2(1-∏/4) Apart from stating the obvious I am stuck on this problem. I think I need to find the equation of the spandrel rather than the circle to even begin solving this problem (something I haven't been able to find nor derive). I have tried to approximate the spandrel by using the equations of a spandrel of nth degree by back calculating the value of n to no avail. Breaking the resultant two shapes into two composite shapes (rectangle and spandrel) seems to make things even more complicated. If anyone can point me in the right direction I would be grateful as I have spent a while thinking about it. This is a problem directed at self study, not homework.