Volume of a Triangular Prism Notes

Published on: September 29, 2026

This Volume of a Triangular Prism Calculator finds the space inside a prism from the base and height of its triangular end and the length of the prism, and shows the working line by line. A prism is the same triangular end repeated along its length, so the area of that end is worked out first and then multiplied by the length. The answer is written in cubic units. Following the same pattern every time is what makes a prism easy to check and repeat.

Triangular prism labeled b, h, ℓ

In the diagram, the triangular end has base \(b\) and height \(h\), and the prism length is \(\ell\).

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the base, the height and the length into the formula.
  4. Multiply the base by the height.
  5. Halve that product to get the area of the triangular end.
  6. Multiply by the length to get the volume.

Formula:

\(V = \frac{1}{2} \times b \times h \times \ell\)
See Example 1 Hide Example 1

Problem

\(b = 9, h = 4, \ell = 8\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the base, the height and the length into the formula.
  4. Multiply the base by the height.
  5. Halve that product to get the area of the triangular end.
  6. Multiply by the length to get the volume.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the volume of a triangular prism whose base is \(b = 9\), whose height is \(h = 4\) and whose length is \(\ell = 8\).

\(b = 9,\; h = 4,\; \ell = 8\)

Step 2

Step 2 - Write the formula.

In this problem: A prism is the same triangular end repeated along its length, so the volume is the area of that triangular end multiplied by the length.

\(V = \frac{1}{2} \times b \times h \times \ell\)

Step 3

Step 3 - Substitute the base, the height and the length into the formula.

In this problem: Replacing \(b\), \(h\) and \(\ell\) with \(9\), \(4\) and \(8\) in \(V = \frac{1}{2} \times b \times h \times \ell\) gives \(V = \frac{1}{2} \times 9 \times 4 \times 8\).

\(V = \frac{1}{2} \times 9 \times 4 \times 8\)

Step 4

Step 4 - Multiply the base by the height.

In this problem: Multiplying the base by the height gives \(9 \times 4 = 36\).

\(V = \frac{1}{2} \times 36 \times 8\)

Step 5

Step 5 - Halve that product to get the area of the triangular end.

In this problem: Halving that product gives the area of the triangular end: \(36 \div 2 = 18\).

\(V = 18 \times 8\)

Step 6

Step 6 - Multiply by the length to get the volume.

In this problem: Multiplying that end area by the length gives \(18 \times 8 = 144\).

\(V = 18 \times 8 = 144\)

Final Answer

\(V = 144\)
See Example 2 Hide Example 2

Problem

\(b = 2.5, h = 6, \ell = 3\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the base, the height and the length into the formula.
  4. Multiply the base by the height.
  5. Halve that product to get the area of the triangular end.
  6. Multiply by the length to get the volume.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the volume of a triangular prism whose base is \(b = 2.5\), whose height is \(h = 6\) and whose length is \(\ell = 3\).

\(b = 2.5,\; h = 6,\; \ell = 3\)

Step 2

Step 2 - Write the formula.

In this problem: A prism is the same triangular end repeated along its length, so the volume is the area of that triangular end multiplied by the length.

\(V = \frac{1}{2} \times b \times h \times \ell\)

Step 3

Step 3 - Substitute the base, the height and the length into the formula.

In this problem: Replacing \(b\), \(h\) and \(\ell\) with \(2.5\), \(6\) and \(3\) in \(V = \frac{1}{2} \times b \times h \times \ell\) gives \(V = \frac{1}{2} \times 2.5 \times 6 \times 3\).

\(V = \frac{1}{2} \times 2.5 \times 6 \times 3\)

Step 4

Step 4 - Multiply the base by the height.

In this problem: Multiplying the base by the height gives \(2.5 \times 6 = 15\).

\(V = \frac{1}{2} \times 15 \times 3\)

Step 5

Step 5 - Halve that product to get the area of the triangular end.

In this problem: Halving that product gives the area of the triangular end: \(15 \div 2 = 7.5\).

\(V = 7.5 \times 3\)

Step 6

Step 6 - Multiply by the length to get the volume.

In this problem: Multiplying that end area by the length gives \(7.5 \times 3 = 22.5\).

\(V = 7.5 \times 3 = 22.5\)

Final Answer

\(V = 22.5\)
See Example 3 Hide Example 3

Problem

\(b = 6, h = 5, \ell = 10\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the base, the height and the length into the formula.
  4. Multiply the base by the height.
  5. Halve that product to get the area of the triangular end.
  6. Multiply by the length to get the volume.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the volume of a triangular prism whose base is \(b = 6\), whose height is \(h = 5\) and whose length is \(\ell = 10\).

\(b = 6,\; h = 5,\; \ell = 10\)

Step 2

Step 2 - Write the formula.

In this problem: A prism is the same triangular end repeated along its length, so the volume is the area of that triangular end multiplied by the length.

\(V = \frac{1}{2} \times b \times h \times \ell\)

Step 3

Step 3 - Substitute the base, the height and the length into the formula.

In this problem: Replacing \(b\), \(h\) and \(\ell\) with \(6\), \(5\) and \(10\) in \(V = \frac{1}{2} \times b \times h \times \ell\) gives \(V = \frac{1}{2} \times 6 \times 5 \times 10\).

\(V = \frac{1}{2} \times 6 \times 5 \times 10\)

Step 4

Step 4 - Multiply the base by the height.

In this problem: Multiplying the base by the height gives \(6 \times 5 = 30\).

\(V = \frac{1}{2} \times 30 \times 10\)

Step 5

Step 5 - Halve that product to get the area of the triangular end.

In this problem: Halving that product gives the area of the triangular end: \(30 \div 2 = 15\).

\(V = 15 \times 10\)

Step 6

Step 6 - Multiply by the length to get the volume.

In this problem: Multiplying that end area by the length gives \(15 \times 10 = 150\).

\(V = 15 \times 10 = 150\)

Final Answer

\(V = 150\)
See Example 4 Hide Example 4

Problem

\(b = 3.5, h = 4, \ell = 6\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the base, the height and the length into the formula.
  4. Multiply the base by the height.
  5. Halve that product to get the area of the triangular end.
  6. Multiply by the length to get the volume.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the volume of a triangular prism whose base is \(b = 3.5\), whose height is \(h = 4\) and whose length is \(\ell = 6\).

\(b = 3.5,\; h = 4,\; \ell = 6\)

Step 2

Step 2 - Write the formula.

In this problem: A prism is the same triangular end repeated along its length, so the volume is the area of that triangular end multiplied by the length.

\(V = \frac{1}{2} \times b \times h \times \ell\)

Step 3

Step 3 - Substitute the base, the height and the length into the formula.

In this problem: Replacing \(b\), \(h\) and \(\ell\) with \(3.5\), \(4\) and \(6\) in \(V = \frac{1}{2} \times b \times h \times \ell\) gives \(V = \frac{1}{2} \times 3.5 \times 4 \times 6\).

\(V = \frac{1}{2} \times 3.5 \times 4 \times 6\)

Step 4

Step 4 - Multiply the base by the height.

In this problem: Multiplying the base by the height gives \(3.5 \times 4 = 14\).

\(V = \frac{1}{2} \times 14 \times 6\)

Step 5

Step 5 - Halve that product to get the area of the triangular end.

In this problem: Halving that product gives the area of the triangular end: \(14 \div 2 = 7\).

\(V = 7 \times 6\)

Step 6

Step 6 - Multiply by the length to get the volume.

In this problem: Multiplying that end area by the length gives \(7 \times 6 = 42\).

\(V = 7 \times 6 = 42\)

Final Answer

\(V = 42\)