Volume of a triangular prism

Definition: The number of cubic units to exactly fill a triangular prism
Try this Change the height and dimensions of the triangular prism by dragging the orange dots. Note how the volume is calculated.

How to find the volume of a triangular prism

Recall that a prism has two congruent, parallel faces called the bases of the prism. The volume of any prism can be found by multiplying the area of one of the bases by its height. In the case of a triangular prism, each base is a triangle.

As a formula where a is the area of one triangular end face, and h is the height.

There are various ways to find the area of the triangle, use whichever method work with what you are given. In the above animation, the three sides are given, so here you would use Heron's Formula. But any method will do - below is a list of methods:

Methods for finding the triangle area

If you know: Use this
Base and altitude "Half base times height" method
All 3 sides Heron's Formula
Two sides and included angle Side-angle-side method
x,y coordinates of the vertices Area of a triangle- by formula (Coordinate Geometry)
Area of a triangle - box method (Coordinate Geometry)
The triangle is equilateral Area of an equilateral triangle

Things to try

  • Drag the three orange dots and note how the volume is calculated
  • Click "hide details", then resize the prism by dragging the three orange dots
  • Calculate the volume yourself
  • Click "show details" to check your answer

Units

Remember that the dimensions and volume will be in the same units. So if the lengths are in centimeters for example, then the volume will be in cubic centimeters (cc).

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