OK, I admit that I did have to rewind and watch the last part twice to get it, but I really liked this proof without words of the area of a circle. Take a look.
If you have trouble seeing what is going on, remember, the outer strand is the circumference, and as we unfold the circle the point of the triangle ends up being where the center of the circle was. Thus the height is exactly the the radius of the circle. Nicely done!