Final answer:
After a dilation with a scale factor of 1/5, the new area of a figure with an original area of 125 square units will be 5 square units, as the area is multiplied by the square of the scale factor (1/25).
Step-by-step explanation:
The question involves a geometric concept known as dilation, which is a transformation that produces an image that is the same shape as the original, but is a different size.
When a figure undergoes a dilation with a given scale factor, the area of the figure is multiplied by the square of that scale factor.
Since the area of the original figure is 125 square units and the scale factor of the dilation is 1/5, you calculate the new area by squaring the scale factor and multiplying it by the original area.
The squared scale factor is (1/5)2 = 1/25. Therefore, the new area will be:
125 units2 × (1/25) = 125/25 units2 = 5 units2
The new area after dilation with a scale factor of 1/5 is 5 square units.