Take the line segment whose endpoints are the points (1,0) and (-1,0) and a point of rotation (x,y).

If the segment is rotated all the way around the point it will trace out an annulus.

Find simplified formula for the area of this annulus in terms of x and y.

Redo this problem for a rectangle with corners at (1,1), (-1,1), (-1,-1), and (1,-1).

While I agree with some of what has been posted so far, the formula given seems to have a problem. 

Consider the origin.  The formula |4pix| gives an area of 0 but the shape traced out is an circle of radius 1.

Posted by Jer on 2010-12-21 10:15:11