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Let $R$ be the radius of the large semicircle and $r$ be the radius of the small semicircle. Reflect the semicircles over $AB$ to get $2$ circles. Then, create a diameter perpendicular to $AB$ . Also, the small semicircle has half the diameter as the large. This diameter can be split at the midpoint of $PQ$ into the lengths $(R+r)$ and $(R-r)$ . This diameter bisects $PQ$ into $2$ segments of length $5$ . By the intersecting chords theorem, $(R+r)(R-r)=5*5=25$ .

Additionally, the difference in the semicircle areas can be expressed as $0.5π(R^2-r^2)$ . By the difference of squares, $(R+r)(R-r)=R^2-r^2=25$ . By substitution, the area between the $2$ semicircles is $12.5π$ which is approximately $39.2$ .