Square, Triangle, And Semicircle Living In Harmony
In the figure above:
The square \(ABCD\) has area 12.25.
\(E\) is the intersection of \(BD\) and the semicircle of diameter \(AD.\)
\(CF\) is a segment drawn from \(C\) and tangent to the semicircle at \(F.\)
Calculate the area of the triangle \(DEF.\) Give your answer to three decimal places.