You can use LEADTOOLS Imaging Pro SDK technology in your application.
You can use the LeadRect struct to see whether two rectangles intersect or not. Either using the Intersect or IntersectsWith methods. The code below adds two rectangles as annotations on a loaded image, finds the intersecting area, then ...
You don't need a 3rd party library to do this. Some built-in libraries will do this nicely.
Draw each rectangle on top of the existing image
Find the intersection of the two rectangles
Draw a third rectangle (perhaps filled with an alpha blend)
Draw a rectangle:
Rectangle ee = new Rectangle(10, 10, 30, 30);
using (Pen ...