To calculate the area of the shaded area, we calculate the difference between the area of the semicircle and the area of the circle.
The formula for area of the semicircle is:
#A_S=(pir_S^2)/2#, where #A_S=#Area of semi-circle, and #r_S^2=#radius of semicircle, given as #12mm# (since #24mm# is the diameter which is twice the radius).
The formula for area of the circle is:
#A_C=pir_C^2#, where #A_C=#Area of circle, and #r_C^2=#radius of circle, calculated as #6mm# (since the radius of the semicircle forms the diameter of the circle, as can be seen in the diagram).
Hence, to calculate the difference between the two, we write:
#A_S-A_C=(pir_S^2)/2-pir_C^2#
#A_S-A_C=(pixx12^2)/2-pixx6^2#
#A_S-A_C=(pixx144)/2-pixx36#
#A_S-A_C=(pixx72)-(pixx36)#
#A_S-A_C=pi(72-36)#
#A_S-A_C=pixx36#
We consider the value of #pi# as #3.141#.
#A_S-A_C=3.141xx36#
#A_S-A_C=113.076#
Since the given diameter is in millimetres, the area will be expressed as square millimetres or #mm^2#.
