(a)

Area of the square wafer is , Where  is its side length.

Here side length is measured in mm.

.

Differentiate on each side with respect to .

.

Substitute in above expression.

.

mm.

This is the rate at which the area is increasing with respect to is  mm²/mm.

(b)

The perimeter of the square is , Where is its side length. 

Consider .

.

Hence rate of change of area with respect to its side length is half of its perimeter.

Geometrical view of square with increased side length .

Therefore area of square with increased side length is .

If is small, then we can approximate .

Rate of change of area of new square with respect to radius can be considered as

(a) mm.

(b) Rate of change of area of a square with respect to its side length is half of its perimeter.