How do you reduce A by 1/2 in the equation A=3.14r^2

Question

How do you reduce A by half in the equation A=3.14r^2

Answer 1

A=πr². Let ½A=πR².

If we divide these two equations we can find the ratio of the radii:

½A/A=½=πR²/πr²=R²/r².

So R²=r²/2, R=r/√2 which is the same as R=r√2/2, or R:r=√2:2

If the area is halved, then the radius is reduced by the factor √½.