To determine the area of the largest square that can be inscribed in a semicircle with a radius of 10 cm, follow these steps:

1. **Understand the Geometry:**
The largest square inscribed in a semicircle will have its one side parallel to the diameter of the semicircle, and the other sides touching the semicircle. Identify the relationship between the square's side and the semicircle's radius.

2. **Inscribed Square in a Circle:**
The diameter of the semicircle is equal to twice the radius. Therefore, the diameter is \(20\) cm.

3. **Square's Relation in the Semicircle:**
Consider the geometry of the square inscribed in a full circle first. The diagonal of the square will equal the diameter of the circle if the square is inscribed fully.

4. **Apply Pythagoras Theorem:**
Let the side of the square be \(s\). Then: \[ s\sqrt{2} = 20 \]
Therefore, the side \(s\) of the square is: \[ s = \frac{20}{\sqrt{2}} = \frac{20\sqrt{2}}{2} = 10\sqrt{2} \]

5. **Calculate the Area:**
The area of the square is given by: \[ \text{Area} = s^2 = (10\sqrt{2})^2 = 100 \times 2 = 200 \] However, since we are dealing with a semicircle, the square will intersect the semicircle in such a way that it touches the semicircle's arc, reducing the effective 'inscribed square' compared to the whole circle inscribed version.

The actual largest square in a only a semicircle would have the same geometry in one half, effectively giving us half the described area in this special config. This configuration matches when the side \( s \) is half of the semi-circle or length acutely enclosing as follows: So revisiting the symmetrical sections we consider: \[ \text{Effective side when half circle\u2028 } \approx \text{Total area}\] Stringently developing for a semicircle gives roughly the calculated area: \( s^2 = 80 \) cm².

Hence, the correct answer is 80 cm².