A rectangle R has a width and length y. A rectangle is formed from by multiplying each of the sides of the rectangle R by 3 as shown in the figure below What is the area of the portion of S lying outside of R?

First, let's determine the area of rectangle R. The area of a rectangle is given by:

Area = Width x Length

In this case, the width of rectangle R is y and the length of rectangle R is also y. Therefore, the area of rectangle R is:

Area of R = y * y = y^2

Next, we will determine the area of rectangle S, which is formed by multiplying each side of rectangle R by 3. Therefore, the width of rectangle S is 3y and the length of rectangle S is 3y. The area of rectangle S is:

Area of S = 3y * 3y = 9y^2

Now, we need to find the area of the portion of S lying outside of R. This can be calculated by subtracting the area of R from the area of S:

Area outside of R = Area of S - Area of R
Area outside of R = 9y^2 - y^2
Area outside of R = 8y^2

Therefore, the area of the portion of S lying outside of R is 8y^2.