Ring Area From A Chord

I'm not sure where this puzzle originated; it's old. Arguably, it is not even a puzzle in the sense that it consists of only a single piece, but it's a great way to annoy your normally-good-at-math friends.

The goal is to __determine the area of the ring formed by the difference between two concentric circles given *only* the length of a chord which is tangent to the inner circle__. In this case, the chord is, as clearly marked, 10cm long.