Ring Area From A Chord

myminifactory

I'm not entirely sure where I first encountered this puzzle; it's certainly old. Perhaps it's not even a traditional puzzle since it basically consists of just one piece, but it's an effective way to frustrate your mathematically-gifted friends. The objective is to calculate the area of the ring formed by the difference between two concentric circles given only the length of a chord that is tangent to the inner circle. In this scenario, the chord, clearly marked at 10cm, serves as the crucial piece of information.