Volume of a Triangular Prism: Formula, Examples and Explanation

The volume of a triangular prism measures the amount of three‑dimensional space the solid occupies. A triangular prism has two identical triangular bases connected by three rectangular faces and every cross‑section parallel to the bases is the same triangle. In total, a triangular prism has 5 faces, 9 edges and 6 vertices. In this guide you’ll learn a clear, step‑by‑step formula for finding the volume, see worked examples and spot everyday objects that are triangular prisms.

Table of Contents

• Volume of Triangular Prism Formula
• How to Calculate Volume of Triangular Prism
• Solved Examples on Volume of Triangular Prism
• Practice Questions on Volume of Triangular Prism
• Frequently Asked Questions of Volume of a Triangular Prism

Volume of Triangular Prism Formula

The idea is to find the area of the flat face at one end, and then stretch that area along the length of the solid.

Volume of a triangular prism = Area of triangular base × Length of the prism

Depending on what information a question gives you, you will need a different formula to find the area of the triangular base. The following table shows the formulas to find the area of the base triangle.

How to Calculate Volume of Triangular Prism

Here are the simple steps to find the volume of a triangular prism:

1. Find the area of the triangular base.
   Identify the type of triangle (right, equilateral, scalene) and use the appropriate area formula (for example, $\tfrac{1}{2}\times\text{base}\times\text{height}$for most triangles).

2. Find the prism’s length.
   This is the distance between the two triangular bases. It’s often called the prism’s height, but don’t confuse it with the height of the triangle itself.

3. Multiply to get the volume.

• Volume = (area of triangular base) × (length of prism).

• Write the answer with cubic units (for example, cm³).
  
  

Solved Examples on Volume of Triangular Prism

Example 1: A rubber door wedge is shaped like a triangular prism. Its triangular face is a right triangle with the two shorter sides measuring 12 cm and 5 cm. The wedge is 20 cm long. What is the volume of the wedge? (Give your answer in cubic centimetres.)

Solution:

Step 1: Area of the triangular base = (1/2) × 12 cm × 5 cm = 30 cm³.

Step 2: Volume = base area × length = 30 cm² × 20 cm = 600 cm³.

So, the door wedge encloses 600 cubic centimetres of rubber.

Example 2: A chocolate bar is shaped like a long triangular prism whose triangular face is equilateral with each side measuring 4 cm. The bar is 21 cm long. What is the volume of the chocolate bar? Give the exact answer in terms of  $\sqrt{3}$​ and an approximate decimal.
Solution:
Area of equilateral triangle = $\frac{\sqrt{3}}{4} \times 4^2 = \frac{\sqrt{3}}{4} \times 16 = 4\sqrt{3} cm².$
Volume = base area × length =  $4\sqrt{3} \times 21 = 84\sqrt{3}​ cm³ ≈ 145.5 cm³.$

Example 3: A ridge tent forms an isosceles triangular prism. The two equal sloping sides of the triangular face are each 5 m, the base across the ground is 6 m wide, and the tent is 4 m deep. What is the volume of the tent (in cubic metres)?
Solution:
For an isosceles triangle with equal sides a = 5 m and base b = 6 m, the area can be found by height: height =  $\sqrt{a^2 - (b/2)^2} = \sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4 m.$
Area = $\frac{1}{2}\times b \times height =\tfrac{1}{2}\times 6 \times 4 =12 m².$
Volume = base area × length =12 \times 4 = 48 m³.

Example 4: A decorative glass paperweight is a triangular prism whose triangular face is scalene with side lengths 13 cm, 14 cm, and 15 cm. The paperweight is 10 cm thick. What is its volume?
Solution:
Semi-perimeter s = $\tfrac{13+14+15}{2}​= 21 cm.$
Area (Heron’s formula) =  $\sqrt{s(s-a)(s-b)(s-c)} = \sqrt{21\times8\times7\times6} = \sqrt{7056} = 84 cm².$
Volume = base area × length = 84×10 = 840 cm³.

Practice Questions on Volume of Triangular Prism

1. A triangular prism has a triangular base with a base of 6 cm and a height of 4 cm. The prism is 10 cm long. What is the volume of the prism?

2. A triangular prism has a triangular base with a base of 8 m and a height of 5 m. The prism is 12 m long. What is the volume of the prism?

3. A tent is shaped like a triangular prism. The triangular end has a base of 3.5 m and a height of 2 m, and the tent is 6 m long. What is the volume of the tent?

4. A triangular prism has a triangular base with a base of 16 cm and a height of 7.5 cm. The prism is 9 cm long. What is the volume of the prism?

5. A triangular prism has a volume of 480 cm³. The triangular base has a base of 12 cm and a height of 8 cm. What is the length of the prism?