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CAHSEE Math Exam: Tutoring Solution21 chapters | 211 lessons

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Lesson Transcript

Instructor:
*Joseph Vigil*

In this lesson, you'll find out what qualities make up a prism and what a pentagonal prism is. You'll also learn the basic properties found in all pentagonal prisms.

Prisms are a certain kind of shape, but what makes them stand out? A **prism** consists of two two-dimensional shapes joined together to form an enclosed three-dimensional shape. For example, a drum is a prism because it has two circles joined together to make the enclosed three-dimensional shape we see here:

In fact, the two-dimensional shape (in this case, a circle) makes the top and bottom, or **faces**, of a prism.

Cans of food, soda cans, and trash cans are all prisms because they're three-dimensional shapes with circular faces. Likewise, boxes are prisms because they're three-dimensional shapes with square or rectangular faces.

Since there are many different shapes that can serve as faces, there are many types of prisms we can make. In fact, prisms are named for the shape of their faces. So a **pentagonal prism** is simply a prism that has pentagons as its faces. Similar to the drum or box, it's an enclosed three-dimensional shape based on two pentagons.

It's very similar to the snare drum, except its bottom and top are pentagons rather than circles.

This image is also a pentagonal prism:

Even though the sides are slanted, it's still a three-dimensional shape based on two pentagons.

Since all pentagonal prisms have the same basic qualities, they all share certain properties:

1. First, all pentagonal prisms have seven sides.

As we can see in this illustration, the five sides of the prism connect the five sides of the pentagons. The top and bottom make sides six and seven.

2. Additionally, all pentagonal prisms have fifteen edges.

In this illustration, the first five edges (or numbers 1-5 in black) form the top pentagonal face, while edges 6-10 (shown in white) form the bottom face. Meanwhile, edges 11-15 (shown in silver) are the 5 edges connecting the pentagonal faces.

3. Finally, all pentagonal prisms have ten vertices, or corners.

There are five corners on both top and bottom where the sides and faces meet, making a total of ten vertices.

**Pentagonal prisms** are simply two pentagons joined together to form an enclosed three-dimensional shape. Because this is true for all pentagonal prisms, they all have:

- 7 sides
- 15 edges
- 10 vertices

The seven sides of a pentagonal prism include the top and bottom, which are known as **faces**.

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11 in chapter 17 of the course:

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CAHSEE Math Exam: Tutoring Solution21 chapters | 211 lessons

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