Finding the Volume of a Triangular Prism

Finding the Volume of a Triangular Prism

Triangular prisms are objects with triangular bases and rectangular sides. This lesson will explore how you can use the formula for the area of a triangle and the height of the prism to find the total volume of the object.

Introduction

Last Mother's Day I decided that I wanted to buy my mom a new bottle of her favorite perfume. After shopping around, I was left with the following two options at the exact same price.

Now, you might notice that both bottles are in an unusual shape. This is called a triangular prism.

A triangular prism is simply a 3D shape that has two triangular bases and three rectangular sides.

In the case of my Mother's Day present, I was left with the task of finding the volume of each triangular prism to determine which bottle would give me the most bang for my buck.

Formula: Volume of a Triangular Prism

After carefully measuring each bottle of perfume I found the following dimensions. Each triangular face is labeled in red and the height of the prisms themselves are labeled in blue.

When it comes to finding the volume of any prism, you might get a little worried over memorizing all of the various formulas and measurements that go along with each. However, a triangular prism is actually very simple to work with! To find its volume, all you need is the area of the triangular base and the height of the prism. So in reality, there really aren't any new formulas you have to mess with. Not too stressful anymore, right?

Remembering back to our formula for the area of a triangle, we know that:

Area = 1/2 b x h

We can use this formula to then find the area of the triangular bases on each perfume bottle.

Looking at the dimensions for bottle A, we see that the triangle has a base of 5 inches and height of 2 inches. Plugging this into our formula for area, we get:

Area = 1/2 b x h

Area = 1/2 x (5) x (2)

Area = 5 sq. in.

Don't forget, area is always measured in square units.

Looking at our dimensions for bottle B, we see that the triangle has a base of 3 inches and height of 2 inches. Plugging this into our formula for area, we get:

Area = 1/2 b x h

Area = 1/2 x (3) x (2)

Area = 3 sq. in.

The last step in finding our volume for each bottle of perfume is to multiply the area of the triangular base by the height of the prism.

For bottle A, we found an area of 5 sq. inches. Multiplying this area by the bottle's height of 3 inches, we get a total volume of 15 cubic inches.

For bottle B, we found an area of 3 sq. inches. Multiplying this area by the bottle's height of 6 inches, we get a total volume of 18 cubic inches.

forget, volume is always measured in cubic units.

Now, looking at our final volumes, we can see that bottle B is the best choice to buy for my mother because she is going to get more perfume for the same price.

Piecing together each step above, the formula for finding the volume of a triangular prism is:

Volume = area of the base x height of the prism

The area of the base is typically noted as an italicized capital, B, while the height of the prism is noted as an italicized lowercase, h. This gives us our final formula:

V = B x h

Let's Give it a Try!

Using the formula we found above, find the volume of the following triangular prism.

Take a minute to find the volume and then scroll down to check your work.

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V = B x h

V = (1/2 x 7 x 3) x 9

V = 10.5 x 9

V = 94.5 cubic cm.