In a triangle $\Delta PQR$, points $A$, $B$, and $C$ are the midpoints of the sides $PQ$, $QR$, and $RP$ respectively. If the area of the triangle $\Delta ABC$ is $16\text{sq.units}$, then the area of the triangle $\Delta PQR$ is:

According to the Midpoint Theorem in geometry, connecting the midpoints of the three sides of a triangle divides the original triangle into four smaller triangles of equal area that are congruent to each other.
Therefore:

$$\text{Area}(\Delta PQR)=4\times \text{Area}(\Delta ABC)$$

$$\text{Area}(\Delta PQR)=4\times 16=64\text{sq.units}$$

Since $64\text{sq.units}$ is not explicitly listed in choices A, B, or C, the correct choice is "None of the above".