[center] [b][/b][/center][b]Introduction[br][br][/b]Finding the total area of the surface of a 3-D shape like a pyramid can be very useful.  It can answer questions like, “How much paint do I need to cover the surface?” or “How much wrapping paper do I need to wrap this container?” There are formulas that you can memorize and use when needed. [b] [/b]However, it is easy to forget a formula that you only use once in a great while. Is there another way to solve a surface area problem without memorizing the formula?  In this [i]GeoGebra [/i]lab you will explore another method for finding surface area. [br][br][b]Step 1.  Create and Experiment a Net[/b] [br][br] Use the MOVE tool [icon]/images/ggb/toolbar/mode_move.png[/icon] and the sliders for[i][b] l [/b][/i](length of base side) and[b][i] h[/i][/b] (height of pyramid) to change the dimensions of the pyramid.  [b][i]S [/i][/b]represents what is called the slant length of the side of a pyramid. [br][br]Now slowly use the [b]Unfold / Fold the Net[/b] slider to create a [b][i]net[/i][/b] of the pyramid.  A net is created by imagining that you cut and unfold the 3-D shape into one, flat shape.  Using the slider, the net can be folded back into the original 3-D shape. [br] [br][b]Step 2.  Find the Surface Area[br][br][/b]Move the [b]Unfold / Fold the Net[/b] slider all the way to the right to completely unfold the pyramid and display the net. The net for a pyramid is a connected set of what two types of polygons?  You already know the method for calculating the area of a square and a triangle.  Use those methods to find the surface area of the entire pyramid.  Explain your solution:   [br][br]Once you have computed the surface area of this pyramid, click on the [b]Check Surface Area Solution[/b] check-box to see the surface area as computed by [i]GeoGebra[/i]. [br][b][br]Step 3.  Practice[br][br][/b]Turn off the [b]Check Surface Area Solution[/b] check-box. Use the sliders to create three pyramids with sides of differing dimensions.  Use the net to help you calculate the surface area of each new pyramid.  Make or print the Data Table shown below.  Fill in the table as you create your pyramids.  Use the [b]Check Surface Area Solution[/b] check-box to check your solutions. [br][br][b]Conclusion[/b] [br][br]For a pyramid,the “official” formula is[b]:  surface area = ( l x 2) + (4) x (1/2 x l x s)[br][br][/b]But if you forget the formula, you can always use reasoning and a net to help you compute the surface area.