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.

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.

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:

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 |

- 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

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).

- Definition and properties of a pyramid
- Oblique and right pyramids
- Volume of a pyramid
- Surface area of a pyramid

- Cylinder - definition and properties
- Oblique cylinders
- Volume of a cylinder
- Volume of a partially filledcylinder
- Surface area of a cylinder

- Definition of a cone
- Oblique and Right Cones
- Volume of a cone
- Surface area of a cone
- Derivation of the cone area formula
- Slant height of a cone

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