Surface Area and the Bigger Picture

April 26th, 2016 

Surface area has always been a concept that I've really struggled with. When I first learned about it, I was in ninth grade Honors Geometry, and it was the most confusing thing I'd ever heard about. The formulas were so difficult for me to remember (in fact, I still don't like using formulas when finding the surface area of a given object), and my teacher insisted we only use the formulas in her class, so I didn't do too well on the test over the subject. I couldn't think of any shortcuts to find surface area, so I just accepted the fact that it wasn't my strong suit and hoped I would never see it again. 

Fast forward to the second semester of my sophomore year of college (also known as this past semester). As I've mentioned, I'm currently taking a math class called Investigating Geometry, Probability and Statistics, which is an Education credit. One day I walked into a class period where we were learning about surface area. A feeling of dread washed over me as I prepared to revisit one of my worst memories associated with math (seriously, I did not like surface area). However, instead of launching straight into formulas with no indication of where they came from, our teacher gave us a worksheet to work on. On the worksheet was a single problem, in which we were asked to find the surface area of a house that was a rectangular prism and had a triangular prism for the roof, with several windows, two garage doors, and one regular door. Because we weren't given any formulas for surface area, I decided to find the area of the walls and the roof, and subtract the areas of the windows and doors as needed. 

Here is the problem. 

I ended up finding the correct surface area of the building and correctly determined how much paint would be needed to paint it. I couldn't believe it took me five years to see that when you're finding the surface area of a three-dimensional object, you can find the area of each of its faces and add them together. After completing this problem, it seemed like such an obvious method of finding surface area, and I was actually mad at myself for not realizing it sooner. 

Surface area stressed me out. Because of this, I had a very narrow mindset on how to solve a surface area problem. I didn't let myself think outside the box and consider different ways to solve a problem. 

As a future educator, I've learned about the importance of being open-minded when it comes to math. Not all of my future students will solve a problem in the exact same way, and that's okay. We all think differently; we all see the world differently. Looking at the big picture and expanding your view when solving a math problem can help lead you to discover new ways to solve things you never thought you've ever come up with, whether those ways are obvious or hidden. 

If you're still struggling with surface area, this website may help you.