The volume of a triangular prism is the total space occupied by the prism in three-dimensional space. We can calculate the volume of the prism by multiplying the area of the base by the height of the prism. We know that triangular prisms have triangular bases, and we also know that the area of any triangle is calculated by multiplying one-half the length of the base by the length of the height.

Here, we will learn about the formula that we can use to calculate the volume of a rectangular prism. Also, we will use this formula to solve some practice problems.

GEOMETRY
formula for the volume of a triangular prism

Relevant for

Learning to calculate the volume of a triangular prism.

See examples

GEOMETRY
formula for the volume of a triangular prism

Relevant for

Learning to calculate the volume of a triangular prism.

See examples

Formula to find the volume of a triangular prism

The volume of a rectangular prism can be found by multiplying the area of the base times the length of the height of the prism. The base of these prisms is a triangle, so we have to find the area of the triangle.

Recall that the area of any triangle is calculated by multiplying the length of the base by the length of the height by one-half. Therefore, we can use the following formula to calculate the volume of a rectangular prism:

V=\frac{1}{2}b\times a\times h

where,

  • b is the length of the triangle’s base
  • a is the length of the height of the triangle
  • h is the length of the height of the prism
diagram of a triangular prism with dimensions

Volume of a triangular prism – Examples with answers

The formula for the volume of triangular prisms is used to solve the following examples. Each example has its respective solution, where the process and reasoning used are detailed.

EXAMPLE 1

A prism has a height of 5 m and its triangular base has a height of 3 m and a base of 4 m. What is its volume?

We have the following lengths:

  • Prism height, h=5
  • Triangle height, a=3
  • Triangle base, b=4

Using these values in the volume formula, we have:

V=\frac{1}{2}bah

V=\frac{1}{2}(4)(3)(5)

V=30

The volume is 30 m³.

EXAMPLE 2

What is the volume of a prism that has a height of 6 m and its triangular base has a height of 5 m and a base of 6 m?

We have the following values:

  • Prism height, h=6
  • Triangle height, a=5
  • Triangle base, b=6

Using the volume formula, we have:

V=\frac{1}{2}bah

V=\frac{1}{2}(6)(5)(6)

V=90

The volume is 90 m³.

EXAMPLE 3

A prism has a height of 8 m and its triangular base has a height of 6 m and a base of 7 m. What is its volume?

We have the following lengths:

  • Prism height, h=8
  • Triangle height, a=6
  • Triangle base, b=7

We substitute these values in the volume formula:

V=\frac{1}{2}bah

V=\frac{1}{2}(7)(6)(8)

V=168

The volume is 168 m³.

EXAMPLE 4

A prism has a height of 11 m and its triangular base has a height of 5 m and a base of 4 m. What is its volume?

From the question, we get the values:

  • Prism height, h=11
  • Triangle height, a=5
  • Triangle base, b=4

Using these values in the volume formula, we have:

V=\frac{1}{2}bah

V=\frac{1}{2}(4)(5)(11)

V=110

The volume is 110 m³.

EXAMPLE 5

What is the volume of a prism that has a height of 9 m and its triangular base has a height of 6 m and a base of 8 m?

We have the following values:

  • Prism height, h=9
  • Triangle height, a=6
  • Triangle base, b=8

Substituting these values in the formula, we have:

V=\frac{1}{2}bah

V=\frac{1}{2}(8)(6)(9)

V=216

The volume is 216 m³.


Volume of a triangular prism – Practice problems

Practice using the formula for the volume of triangular prisms to solve the following problems. If you need help with this, you can look at the solved examples above.

A triangular prism has a height of 7m and a triangular base with a base of 4m and a height of 3m. What is its volume?

Choose an answer






A triangular prism has a height of 8m and a triangular base with a base of 5m and a height of 5m. What is its volume?

Choose an answer






A triangular prism has a height of 12m and a triangular base with a base of 8m and a height of 5m. What is its volume?

Choose an answer







See also

Interested in learning more about triangular prisms? Take a look at these pages:

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