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 "Triangular Prism." Move the three sliders – Width, Depth, and Height – to change the size of the triangular prism.

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

Use the sliders and create a triangular prism whose dimensions are Base Width 6, Prism Height 10, and Base Depth 4. Click on the triangular prism to rotate it and view it from several angles.

Answer the following questions. Click on the blank space to check your answers.

• How many faces does your prism have this time? Interactive popup. Assistance may be required.

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  5

• What do the 6 and 4 measures represent on the triangular prism? Interactive popup. Assistance may be required.

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  The base and height of the triangles at both ends.

• Why do you think these were referred to as "base width" and "base depth"? Interactive popup. Assistance may be required.

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  The triangles are the "bases" of the prism.

• Why is one of the rectangular sides not the base of the prism? Interactive popup. Assistance may be required.

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  The rectangular side does not have another congruent rectangle that is parallel to it within the figure.

• Look at the bottom of the screen. To the right of the sliders, what is the total surface area of the triangular prism? Interactive popup. Assistance may be required.

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  184.0 units²

Another way of viewing the total surface area of a rectangular prism, is by selecting the "Width by Depth" above the prism.

• Count the squares on the face. Interactive popup. Assistance may be required.

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  12 units²

• The mathematical term for the number of squares in the triangle is Interactive popup. Assistance may be required.

  _______________.

  area

• The formula for the area of a triangle is Interactive popup. Assistance may be required.

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  A = 1 2 bh

• Find the area of the triangle using the formula. Interactive popup. Assistance may be required.

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  1 2 (6 x 4) = 1 2 (24) = 12 units²

• There are Interactive popup. Assistance may be required.

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  2

• The total surface area for these congruent faces is Interactive popup. Assistance may be required.

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  2 x 12 units² = 24 units ²

Use your mouse and turn the prism so that the rectangular face with a width of five units is showing.

• The rectangle's dimensions are Interactive popup. Assistance may be required.

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  10
  and Interactive popup. Assistance may be required.

  _______________.

  5

• The area or the number of square units of this face is Interactive popup. Assistance may be required.

  _______________.

  10 x 5 = 50 units²

• There are Interactive popup. Assistance may be required.

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  2

• The total surface area for these congruent faces is Interactive popup. Assistance may be required.

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  2 x 50 units² = 100 units²

Use your mouse and turn the prism so that the rectangular face with a width of six units is showing.

• The rectangle's dimensions are Interactive popup. Assistance may be required.

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  10
  and Interactive popup. Assistance may be required.

  _______________.

  6

• The area or the number of square units of this face is Interactive popup. Assistance may be required.

  _______________.

  10 x 6 = 60 units²

• There are Interactive popup. Assistance may be required.

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  1

• The total surface area for these congruent faces is Interactive popup. Assistance may be required.

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  60 units²

• The total surface area of the triangles is Interactive popup. Assistance may be required.

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  24 units²

• The total surface area of the first set of rectangles is Interactive popup. Assistance may be required.

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  100 units²

• The total surface area of the second rectangle is Interactive popup. Assistance may be required.

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  60 units²

• Using the calculations above, how could you find the total surface area of the triangular prism? Interactive popup. Assistance may be required.

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  Add the areas of all the faces.

• Find the total surface area of the triangular prism. Interactive popup. Assistance may be required.

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  24 units² + 100 units² + 60 units² = 184 units²