We need to understand what surface area represents.
Surface area, as it suggests, refers to the total amount of area around its surface. In other words, we are not finding how much it can hold (volume), but rather, how much space we have around the box.
Now, we are given it is closed so we need to include the tops, as well.
For Package A, the front and back of the box has an area of 14 inches by 12 inches. So, we start with:
[tex]A_1: 2(14 \cdot 12)[/tex]
Now, let's look at the sides of the box. The sides of the box measure 12 inches by 3 inches.
Hence, we have the two sides' area to be:
[tex]A_2: 2(12 \cdot 3)[/tex]
Lastly, we need to look at the top and bottom.
We can see that they have dimensions 14 inches by 3 inches.
[tex]A_3: 2(14 \cdot 3)[/tex]
Now, our total surface area is just all three areas added together.
Thus, [tex]SA_A: A_1 + A_2 + A_3[/tex]
[tex]SA_A: 2(168) + 2(36) + 2(42)[/tex]
[tex]SA_A = 492 in^{2}[/tex]
Now, you just repeat for Package B and compare the two surface areas to find which one is larger.
