After clicking on the image below, find the three sliders underneath the object. There are three additional topics in the second column, make sure the last drop down menu shows "Rectangular Prism." Move the three sliders – Width, Depth, and Height – to change the size of the rectangular prism.

Source: Interactivate: Surface Area and Volume, Shodor.org

Use the sliders at the bottom of the screen to create a cube with a Width, Depth, and Height of 9. Change the sliders to create a rectangular prism whose dimensions are Width 2, Depth 5, and Height 8. Answer the following questions. Click on the blanks to check your answers.

• Which face is congruent to the top? Interactive popup. Assistance may be required.

  _______________

  the bottom

• Which face is congruent to the front? Interactive popup. Assistance may be required.

  _______________

  the back

• Which face is congruent to the right side? Interactive popup. Assistance may be required.

  _______________

  the left side

• There are a total of Interactive popup. Assistance may be required.

  _______________

  6

• What is the total surface area of your prism? Interactive popup. Assistance may be required.

  _______________

  132.0 units²

Finding the Total Surface Area mathematically:

1. Click on the rectangular prism. Using your mouse, turn your prism so that the long narrow side is in the front. Its dimensions are 2 and 8. (Width and Height)

• How many square units are on this face? Interactive popup. Assistance may be required.

  ________________

  16 units²

• How many faces on the prism will be this size? Interactive popup. Assistance may be required.

  ________________

  2

• What will be the total surface for these congruent faces? Interactive popup. Assistance may be required.

  ________________

  32 units²

2. Turn your prism so that the shorter, but still narrow, side is in the front. Its dimensions are 2 and 5. (Width and Depth)

• How many square units are on this face? Interactive popup. Assistance may be required.

  _______________

  10 units²

• How many faces on the prism will be this size? Interactive popup. Assistance may be required.

  _______________

  2

• What will be the total surface area for these congruent faces? Interactive popup. Assistance may be required.

  _______________

  20 units²

3. Turn your prism so that the largest side is in the front. Its dimensions are 5 and 8. (Depth and Height)

• How many square units are on this face? Interactive popup. Assistance may be required.

  _______________

  40 units²

• How many faces on the prism will be this size? Interactive popup. Assistance may be required.

  _______________

  2

• What will be the total surface area for these congruent faces? Interactive popup. Assistance may be required.

  _______________

  80 units²

• Use the calculations above to describe the next step and find the total surface area of the entire rectangular prism? Interactive popup. Assistance may be required.

  _______________

  Add all the total surface areas above, 32 + 20 + 80 = 132 sq units

Journal Entry

If you keep the depth and width the same, but change the height, what do you think will happen to the surface area of the rectangular prism? Return to the Surface Area and Volume applet and verify your answer!