2012 HMMT November General Round Problem 3

ABCD is a rectangle with AB = 20 and BC = 3. A circle with radius 5, centered at the midpoint of DC, meets the rectangle at four points: W, X, Y, and Z. Find the area of quadrilateral WXYZ.

Answers are checked by value, so any equivalent form is accepted: 1/2, \frac{1}{2} and 0.5 all count as the same answer.

Full credit goes to HMMT for authoring these problems. This problem is from the November 2012 contest; the official solution is available on the HMMT archive. HMMT is not affiliated with or endorsing TopsOJ in any way.