(c) $\dfrac{1}{8}\pi d^2$
A semi-circle has $\theta = 180°$ and radius $r = d/2$. Area $= \dfrac{180}{360} \times \pi \left(\dfrac{d}{2}\right)^2 = \dfrac{1}{2} \times \dfrac{\pi d^2}{4} = \dfrac{\pi d^2}{8}$.
Use the sector area formula $\dfrac{\theta}{360} \times \pi r^2$ with $\theta = 180°$ and $r = d/2$. A common mistake is using $d$ directly as the radius — remember $r = d/2$, which when squared gives $d^2/4$, and the factor of $\frac{1}{2}$ (from $\frac{180}{360}$) gives $\frac{1}{8}\pi d^2$.