Final answer:
When the base and height of a rectangle are both multiplied by 1/5, the new area is 1/25 of the original area. Since the area is calculated as base times height, reducing both dimensions by a factor of 1/5 reduces the area by a factor of 1/25.
Step-by-step explanation:
To determine the effect of change on the area of the rectangle when the base and height are both multiplied by 1/5, we can look at the formula for the area of a rectangle. The area (A) of a rectangle is calculated by multiplying its base (b) by its height (h), so A = b x h. If both the base and the height of a rectangle are multiplied by 1/5, then the new area (A') becomes (1/5)b x (1/5)h. This simplifies to A' = (1/25)(b x h).
Applying this to original dimensions, if A = b x h originally, when both are reduced by a factor of 1/5, the new area is reduced by a factor of 1/25, which means the new area is just 1/25 of the original area. For example, if the original area of a rectangle is 100 square units, the new area after the change would be 100 x (1/25) = 4 square units.