Your thinking is correct and the simplest, but it is wrong.

The correct one should be

Shadow area =2* semicircle area -2*( 1/3 semicircle area)+equilateral triangle area with side length as radius.

= area of circle -65438+ 0/3 area of circle+area of equilateral triangle with radius.

The method of finding the triangle area may have been learned in primary school, that is: base * height /2.

The key high value is 2√3, which may be beyond the scope of primary schools.