1. The problem states that a figure has a perimeter of 40 units and an area of 100 units squared. We want to find the new perimeter and area after the figure is dilated by a scale factor of $\frac{1}{2}$. 2. When a figure is dilated by a scale factor $k$, the perimeter changes by a factor of $k$ and the area changes by a factor of $k^2$. 3. Given the original perimeter $P = 40$ units and area $A = 100$ units$^2$, and scale factor $k = \frac{1}{2}$: $$\text{New perimeter} = k \times P = \frac{1}{2} \times 40 = 20 \text{ units}$$ $$\text{New area} = k^2 \times A = \left(\frac{1}{2}\right)^2 \times 100 = \frac{1}{4} \times 100 = 25 \text{ units}^2$$ 4. Therefore, the new perimeter is 20 units and the new area is 25 units squared. 5. Among the options given, the correct one is: Perimeter: 20 units; Area: 25 units$^2$.