Answer:
The new area will be 1/4 of the old area.
Explanation:
If you don't know the answer already from (1/2)^2 = 1/4, you can figure it out.
new area = (1/2·5 mm)·(1/2·5 mm) = (1/2)^2·(5 mm)^2
old area = (5 mm)·(5 mm) = (5 mm)^2
Then the ratio of new area to old area is ...
((1/2)^2·(5 mm)^2)/(5 mm)^2 = (1/2)^2 = 1/4
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When any plane figure has its linear dimensions scaled by a factor of "s", its area will be scaled by a factor of s^2.
Here, s=1/2, and s^2 = 1/4, the ratio of new area to old.