I always wonder how people got the formula pi*r^2 as area of circle. So I launched firefox and started googling about area of circle, there are many pages which explains formula but none of them easy to understand. Finally I end-up with a page which explains the formula with real life example.
Original Source: The real story behind the "Area of a Circle"
A circle can be seen as collection of triangles. Unwrap the triangles and we get a strip of triangles. Now fold the triangle strip so that it will form a rectangle. In this rectangle the height is approximately the radius of circle and the length of rectangle is half of the circle's circumference. Now the area of the rectangle is = width x length = r * (pi*r) hence the are of circle is pi*r^2.