Surface Area: Intuitive Introduction

Author:: Emily Munroe, Tim Brzezinski

Topic:: Area, Surface

STUDENTS:

Interact with the applet below for several minutes. Make sure you use the "Create Net" feature and the "Options" feature and that you turn on the "Filling" feature. After doing so, please answer the questions that follow.

Create a rectangular prism that has a length = 4 units, width = 5 units, and height = 3 units.

1. Use the applet to the to find out...

1a) How many square units (i.e. "squares") appear on each pink face? How many total? 1b) How many square units (i.e. "squares") appear on each gold face? How many total? 1c) How many square units (i.e. "squares") appear on each white face? How many total?

Check my answer

2. Use your answers from question 1 to determine the TOTAL SURFACE AREA of this rectangular prism.

That is, how many square units, or squares, cover the ENTIRE SURFACE of this rectangular prism? Hint: Slide the "Create Net" feature all the way to the right. Hint: Think about how many facesthe figure has total.

Check my answer

Now create a rectangular prism that has a length = 8 units, width = 3 units, and height = 5 units.

3. Use the applet to find out...

3a) How many square units (i.e. "squares") appear on each pink face? 3b) How many square units (i.e. "squares") appear on each gold face? 3c) How many square units (i.e. "squares") appear on each white face?

4.Use your answers from question 3 to determine the TOTAL SURFACE AREA of this rectangular prism.

That is, how many square units, or squares, cover the ENTIRE SURFACE of this rectangular prism?

5. How is the TOTAL SURFACE AREA of a rectangular prism determined?

Without looking up anything on another tab in your internet browser, DESCRIBE how we can determine the total surface area (number of squares) that cover the entire surface of this rectangular prism. Be specific! Bonus: Come up with the algebraic formula. - EXPLAIN your answer