Charla completes \( \frac{2}{3} \) of the area in \( \frac{1}{2} \) hour. To find out how long it will take her to complete the entire area, we can set up a proportion.
If \( \frac{2}{3} \) of the area takes \( \frac{1}{2} \) hour, then the whole area (1 whole, or \( \frac{3}{3} \)) will take:
\[ \text{Time for the whole area} = \left(\frac{1}{2} \text{ hour}\right) \div \left(\frac{2}{3}\right) = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \text{ hour} \]
Therefore, it will take Charla \( \frac{3}{4} \) of an hour to complete the entire picture.