As you’ve said, the area is Pi*r^2. To simplify things slightly: r=d/2 ==> Area = Pi*r^2 = Pi*(1/4)*d^2. If the diameter is reduced by x percent then the new diameter will be (1-(x/100))*d (where d is still the original diameter). Now, plugging this new bit into the formula relating diameter and area gives you:
New area = Pi*(1/4)*((1-(x/100))*d)^2
=Pi*(1/4)*(d^2)*(1-(x/100))^2
= Original area * (1-(x/100))^2
Is that what you’re after?
Edit: damn, beaten to it 😛