The moment of inertia of a uniform semicircular disc of mass $M$ and radius $r$ about a line perpendicular to the plane of the disc through the centre is:

The moment of inertia of a complete disc of mass $M^{\prime }$ and radius $r$ about the central perpendicular axis is $I=\frac{1}{2}{M}^{\prime }{r}^2$.A semicircular disc can be thought of as half of a complete disc. If the mass of the semicircle is $M$, the mass of the full disc would be $2M$.
$$I_{full}=\frac{1}{2}(2M)r^2=M{r}^2$$
The moment of inertia is an additive property. The $I$ for the semicircle is half of the $I$ for the full disc (of mass $2M$):
$$I_{semi}=\frac{1}{2}{I}_{full}=\frac{1}{2}M{r}^2$$