How many times will the area of a square increase if its side is increased 4 times?

1. A square is an equilateral rectangle.

Accordingly, the area of a square is equal to the size of its side squared.

That is, S = a * a, where a is the side of the square

2. Let’s denote the area of the square X, and the area of the square with the side increased by 4 times Y.

3. Let’s calculate the ratio of the areas of two squares:

Y / X = (4a * 4a) / a * a

4. Let’s shorten the following:

Y / X = 16 (a * a) / a * a = 16

Answer: the area of the square will increase 16 times.