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Sides of a Triangle are all Diameters of Semicircles : Area of Shaded Region?

Triangle ABC is a right triangle in a semicircle with AC as a diameter. Semicircles are also drawn with legs AB and BC as diameters.
If AB=12 and BC = 5, What is the sum of the shaded areas? Please see the attached diagram.


Solution Preview

Solution. Since AB=12 and BC = 5, we have AC=13 (since AC^2=AB^2+BC^2)

The area S1 of semicircle with diameter AB=12 is ...

Solution Summary

When the sides of a triangle are all diameters of semicircles, the area of a shaded region is found.