Q) In the picture we have a semi-circle inscribed in a rectangle. We see that the diameter is equal to the width of the rectangle (the horizontal side) of the rectangle (w), so we have:
[tex]d=w=6\operatorname{mm}[/tex]From the fact that the diameter is always two times the radius for every circle, we have:
[tex]r=\frac{d}{2}=\frac{6}{2}\operatorname{mm}=3\operatorname{mm}[/tex]Now, we also see from the picture:
[tex]h=r=3\operatorname{mm}[/tex]The question asks us about the area of the shaded region.
A) The shaded region can be computed in the following way:
1) First, we compute the area of the rectangle (Ar).
[tex]A_r=w\cdot h=6\operatorname{mm}\cdot3\operatorname{mm}=18mm^2[/tex]2) Secondly, we compute the area of the semi-circle (Asc), which is half of the area of the entire circle.
[tex]A_{sc}=\frac{1}{2}\cdot A_c=\frac{1}{2}\cdot\pi\cdot r^2=\frac{1}{2}\cdot3.14\cdot(3\operatorname{mm})^2=14.13mm^2[/tex]3) Finally, we compute the area of the shaded region taking the difference between the area of the rectangle and the area of the semi-circle.
[tex]A_s=A_r-A_{sc}=18mm^2-14.13mm^2=3.87mm^2[/tex]