Example: A Triangular Prism

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

• The base of the prism is a

  Interactive popup. Assistance may be required.

  _______________.

  triangle

• The formula for the area of a triangle is

  Interactive popup. Assistance may be required.

  _______________.

  A = 1 2 bh

• To find the volume of the prism the Interactive popup. Assistance may be required. _______________ area of the triangular base is multiplied by the Interactive popup. Assistance may be required. _______________ height of the prism or Interactive popup. Assistance may be required. _______________ V = B∙h =( 1 2 b∙h)∙h .

If the base of the prism is a hexagon, the volume is still found using the formula V = B∙h.

Example

A builder is building a house that will sit 4 feet above ground on concrete support pilings that are buried 2 feet into the ground. The concrete will be poured into wooden forms that are in the shape of hexagonal prisms. The builder must know the amount of concrete to buy in order to have enough to pour the pilings. His sketch is shown below.

How many cubic feet of concrete must the builder order in order to fill 20 pilings like the one show in his sketch?

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

• The formula for volume is Interactive popup. Assistance may be required. _______________ V = B∙h where Interactive popup. Assistance may be required. _______________ B is the area of the hexagonal base.
• The area of the Interactive popup. Assistance may be required. _______________ hexagonal base is found by using the area of a triangle.

• The base is made up of Interactive popup. Assistance may be required. _______________ 6 equilateral triangles.
• The formula for the area of a triangle is Interactive popup. Assistance may be required. _______________ A = 1 2 bh where b and h are the base and height of one equilateral triangle.
• The area of the hexagonal base can be found using the formula Interactive popup. Assistance may be required. _______________ B = 6( 1 2 bh) .
• The area of the hexagonal base is Interactive popup. Assistance may be required. _______________ B = 6( 1 2 bh) = 6( 1 2 ∙ 6 ∙ 4) = 6(12) = 72 sq in .
• The problem is asking for the cubic feet of concrete needed to fill the hexagonal prism. The Interactive popup. Assistance may be required.

  _______________ .

  volume of the hexagonal prism needs to be found.
• The formula for the volume of a prism is

  Interactive popup. Assistance may be required.

  _______________.

  V = B∙h

• The height of the hexagonal prism is

  Interactive popup. Assistance may be required.

  _______________.

  6 feet

• The base is in square Interactive popup. Assistance may be required. _______________ inches and the height is Interactive popup. Assistance may be required. _______________ feet .
• The height needs to be converted into Interactive popup. Assistance may be required. _______________ . inches

• Six feet equals Interactive popup. Assistance may be required. _______________. 6 x 12 = 72 inches Therefore h, the height of the prism, is Interactive popup. Assistance may be required. _______________ 72 inches .
• Find the volume by substituting the values into the formula

  Interactive popup. Assistance may be required.

  _______________.

  V = B∙h = 72 ∙ 72 = 5184 cubic in

The builder needs to purchase enough cement to pour 20 pilings. Cement is measured in cubic feet.

• The volume needs to be converted from Interactive popup. Assistance may be required. _______________ cubic inches to Interactive popup. Assistance may be required. _______________ cubic feet .
• There are Interactive popup. Assistance may be required. _______________
  12 inches in one foot.
• There are Interactive popup. Assistance may be required. _______________
  12 x 12 x 21 = 1728 cubic inches in one cubic foot.
• To change the volume from cubic inches to cubic feet Interactive popup. Assistance may be required. _______________ divide the volume by 1728 cubic inches.
• One piling is Interactive popup. Assistance may be required. _______________ 5184 ÷ 1728 = 3 cubic feet.
• The builder needs 20 pilings, each piling requires Interactive popup. Assistance may be required. _______________ 3 cubic feet of concrete.
• The builder will need Interactive popup. Assistance may be required. _______________ 3 x 20 = 60 cubic feet of concrete.

Watch a video of more examples of finding the volume of prisms.