50 POINTS! Carol is designing an artistic picture frame, which she wants to sell online. The picture frame will be square, but will come in several different sizes. She plans to place decorative stones around the outside of the picture frame. Carol’s first step was creating this prototype frame. (The first picture attached) You will be helping Carol form expressions that will tell her the number of stones she’ll need to order for each frame.

Part A:
How many stones make up the perimeter of the prototype picture frame? Perimeter is usually calculated by adding the length of each side of a shape. In the prototype, there are four stones per side. If we try to find the total number of stones in the frame by adding the number of stones per side, we’ll get an incorrect total. Why?

Part B:
Suppose that s equals the number of stones on one side of the picture frame. Write an expression that would give the number of stones in the top and bottom sides together.

Part C:
Write an expression in terms of s that represents the remaining stones. (The second attached picture) Write an expression in terms of s that represents the remaining stones.

Part D:
Now combine the two expressions you wrote in parts b and c by adding them together. What does the expression formed by this operation represent?