Experiment with finding the volume area of a triangular prism by clicking on the image below.

In the second column change the drop down menu to "Triangular Prism" and change the dimensions to base width: 6, base depth: 4, and prism height: 10.

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

Source: Surface Area and Volume, Shodor.org

Rotate the prism and look at it carefully.

• The triangular prism has Interactive popup. Assistance may be required. _______________
  5 faces.
• The 6 and 4 are labeled as "base width" and "base depth" because they are the Interactive popup. Assistance may be required. _______________ base and Interactive popup. Assistance may be required. _______________ height of the triangle Interactive popup. Assistance may be required. _______________ bases
  of the prism.
• The rectangular sides are not the bases of the prism because the Interactive popup. Assistance may be required. _______________ rectangular side does not have another congruent Interactive popup. Assistance may be required. _______________ rectangle that is parallel to it.
• The volume of the triangular prism is

  Interactive popup. Assistance may be required.

  _______________

  120.0 cubic units

Finding the Volume Mathematically

Click on the triangular prism. Using your mouse, turn your prism so one of the triangular faces is in the front. Its dimensions are 6 and 4. (Base width and depth).

• To find the square units on this face use the area formula for a triangle.

  Interactive popup. Assistance may be required.

  _______________

  A = 1 2 bh

• How many square units are on this face?

  Interactive popup. Assistance may be required.

  _______________

  A = 1 2 bh = 1 2 (6)(4) = 12 units²
  This is a single layer of blocks.
• How many layers of this size are needed to construct the prism of this size?

  Interactive popup. Assistance may be required.

  _______________

  10

• Find the total cubic units in the layers or the volume.

  Interactive popup. Assistance may be required.

  _______________

  12 x 10 = 120 cubic units

Note: The volume is in cubic units.

Turn your prism so that one of the rectangular faces is in the front. Its dimensions are 10 and 5.

• Find the area of this face.

  Interactive popup. Assistance may be required.

  _______________

  50 units²

• In the triangular prism, how many layers will be this size?

  Interactive popup. Assistance may be required.

  _______________

  1

• Can the product of 50 and the height of the triangular face be the volume of the prism, why or why not?

  Interactive popup. Assistance may be required.

  _______________

  No. All the layers are not the same size.

• This example shows the importance of the

  Interactive popup. Assistance may be required.

  _______________

  bases