The statement a is p percent of b represents the proportion where b is base, a is a part of the base and is the percent.

Let x is the side length of a smaller square and y is the side length of a larger square.

The word the side length x of a smaller square is 40% of the the side length y of a larger square represent the proportion .

Simplification of proportion is .

The area formula of a square is .

The area of smaller square is and the area of larger square is .

The word the ratio of area of a smaller square to area of a larger square represent the proportion .

Substitute the value of in the proportion .

To calculate the percentage, multiply the number by 100.

Therefore

Cancel common terms.

Multiply each side by term .

Cancel common terms.

.

The equation represent the words the area of a smaller square is 16% of the area of the larger square.

No, the area of a smaller square does not 40% of the area of the larger square.