Area of 2 semicircle - area of triangle.
Area of big semicircle
= ½×π×10²
= 50π
Area of small semicircle
= ½×π×8²
= 32π

Area of △ = ½×20×16 = 160
Shaded area
= 50π+32π-160
= ( 82π-160 )cm²

Student, the idea behind this calculation is :

When you add the two semicircle areas together, the middle part overlaps.

So you have two of that part now.


Subtracting the triangle area means cutting out some of the areas that were not overlapping , so they become white/unshaded now.


But it is also removing one of the two copies of the overlapping part.


So what you have left are some of the outer shaded parts that didn't overlap, plus 1 overlapping part