# Surface Area of Right Prisms

Warmup

Move each slider to see how that affects the size and therefore Surface Area of the prism(Cuboid).

Activity #1

Understand Total Surface Area of a Prism.

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, answer the questions that follow. • Create a rectangular prism that has a length = 4 units, width = 5 units, and height = 3 units.

(1.) how many square units (i.e. “squares”) appear on each pink face? How many total?

(2.) how many square units (i.e. “squares”) appear on each gold face? How many total?

(3.) how many square units (i.e. “squares”) appear on each white face? How many total?

(4.) Use your answers from question 1, 2, & 3 above to determine the TOTAL SURFACE AREA of this rectangular prism. Hint: Slide the “Create Net” feature all the way to the right.

Now create a rectangular prism that has a length = 8 units, width = 3 units, and height = 5 units. Use the applet to the to find out

(1.) how many square units (i.e. “squares”) appear on each pink face? How many total?

(2.) how many square units (i.e. “squares”) appear on each gold face? How many total?

(3.) how many square units (i.e. “squares”) appear on each white face? How many total?

(4.) Use your answers from question 1, 2, & 3 above to determine the TOTAL SURFACE AREA of this rectangular prism. Hint: Slide the “Create Net” feature all the way to the right.

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

Activity #2

Explore Ways to Calculate Total Surface Area of a Prism.

Here below is a picture a prism. Three students are trying to calculate the surface area of this prism. Noah says, “This is going to be a lot of work. We have to find the areas of 14 different faces and add them up.”

Elena says, “It’s not so bad. All 12 rectangles are identical copies, so we can find the area for one of them, multiply that by 12 and then add on the areas of the 2 bases.”

Andre says, “Wait, I see another way! Imagine unfolding the prism into a net. We can use 1 large rectangle instead of 12 smaller ones.”

(1.) Do you agree with any of them? Explain your reasoning.

(2.) How big is the “1 large rectangle” Andre is talking about? Explain or show your reasoning. If you get stuck, consider drawing a net for the prism.

(3.) Will Noah’s method always work for finding the surface area of any prism? Explain your reasoning.

(4.) Will Elena’s method always work for finding the surface area of any prism? Explain your reasoning.

(5.) Will Andre’s method always work for finding the surface area of any prism?  Explain your reasoning.

(6.) Which method do you prefer? Why?

(7.) Use each of these two methods to find the surface area of the prism.

(a.) Adding the areas of all the faces.

(b.) Using the perimeter of the base.

Challenge #1

Use your chosen method to calculate the surface area of the prism in the applet below. Show your thinking. Organize it so it can be followed by others.

Challenge #2

In a deck of cards, each card measures 6 cm by 9 cm.

(1.) When stacked, the deck is 2 cm tall, as shown in the first photo. Find the volume of this deck of cards.

(2.) Then the cards are fanned out, as shown in the second picture. The distance from the rightmost point on the bottom card to the rightmost point on the top card is now 7 cm instead of 2 cm. Find the volume of the new stack.

Quiz Time