Measure to Measure

Formula for Surface Area

How should we find the surface area of the box? One could find the area of each side of the box, then add the values together. However, there is an easier way. Remember our measurement for the area of the original piece of paper? 475 square units, right? We used that same piece of paper to make our box. What did we change?

We cut 4 3x3 squares out of it. The example box had a cut of 3, but the other boxes had different cuts. The size of the cut is something that we chose or determined ahead of time, and is known as an independent variable.

We will have our surface area if we subtract the area we cut out from the area we started out with. To find the area we cut out, we must simply multiply the cut times itself, for example 3 times 3 (or 3²) to get the area of each cut out square, and then multiply that value by 4, or the number of these squares that we cut out.

This procedure can be represented as a formula for surface area: SA = 475-4*cut². For a cut of 3, you should find that this formula gives a surface area is 439 square units. The surface area you get depends on which cut you choose, so it is known as a dependent variable. For general formulas, x represents the independent variable and y represents the dependent variable.

Surface Area   =   original area   -   # of squares   *   size of squares   y = 475 - 4 * x2