Volume and Surface Area of a Prism
11 Examples!

In this geometry lesson, we’re going to deep dive into prisms.

Specifically, you’re going to learn how to find the volume and surface area of a prism.

So let’s get started!

A prism is a polyhedron with two congruent, parallel faces, called bases.

I like to think of them as the “top” and “bottom” of the prism.

The other faces of a prism are called lateral faces, and they are parallelograms formed by connecting the corresponding vertices of the bases together.

The altitude, or height, of a prism is the perpendicular distance between the two bases. And as Math Bits Notebook accurately states, in a right prism, the height is a lateral edge whereas, for an oblique prism, the height is the shortest line segment between the bases.

So what’s the point?

To find the surface area and volume of these three-dimensional solids.

To find the surface area of a prism, we must add the area of each face. Thankfully there is a formula for finding the surface area of a right prism that makes our calculations fast and efficient, as seen below.

What is important to note is that the surface area of a right prism is the sum of the lateral area, sometimes called the net, and twice the area of a base.

And to find the volume of a right prism, we simply find the product of the area of the base and the height of the prism.

Here is an example that demonstrates how to find the surface area and volume of a prism, and really highlights both of these formulas above.

In the video below, you’ll learn how to find:

• Lateral area
• Surface area
• Volume for right prisms
• Volume of composite or complex prisms using the volume addition postulate

Video – Lesson & Examples

58 min

• Introduction to prisms
• 00:00:23 – What is a prism? formulas for lateral area, surface area, and volume
• Exclusive Content for Member’s Only

• 00:10:38 – Find the surface area and volume for each prism (Examples #1-6)
• 00:17:16 – Use the volume addition postulate to find the volume of the polyhedron (Examples #7-8)
• 00:17:16 – Determine the number of gallons of water in a swimming pool given its volume (Example #9)
• 00:17:16 – Find the surface area of a right rectangular prism (Example #10)
• 00:17:16 – Find the surface area of an oblique prism (Example #11)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions