## Surface Area of a Prism

## Opening

# Surface Area of a Prism

- What is the surface area of this rectangular prism?
- Explain how you found the surface area.

- What is the surface area of this rectangular prism?
- Explain how you found the surface area.

Explore and apply the method for finding the surface area of a right prism.

The top and bottom faces of a prism are the bases. The remaining faces are the lateral faces. Notice that the lateral faces form one large rectangle. This rectangle is called the *lateral surface*.

Use the Prism Net interactive to explore the net of a rectangular prism. Notice that as you change the net, the faces of the prism adjust accordingly.

- How do you think the perimeter of the base and the length of the lateral surface are related?
- Why do you think the perimeter of the base and the length of the lateral surface are related in this way?
- How could you find the area of the lateral surface?
- Based on your observations about lateral surface area, describe a method for finding the surface area of a rectangular prism.

INTERACTIVE: Prism Net

- What are the width and length of the lateral surface, and how could you use those measurements to find the area of the lateral surface?

Find the surface area of this regular pentagonal prism.

- How long is the lateral surface? How wide is the lateral surface?
- Use this information to find the surface area of the prism.
- Explain the steps you used.

Describe how to find the surface area of a right prism. Support your thinking with examples.

A square prism has a height of 3 ft and a volume of 48 ft${}^{3}$. What is the total surface area of the prism?

Take notes about your classmates’ explanations for finding the surface area of a right prism.

As your classmates present, ask questions such as:

- How did you find the formula for the surface area of a prism?
- How is the formula similar to the formula for the surface area of a rectangular prism?
- How do you think volume and surface area of a right prism are related?

Each drawing shows the base of a prism. Find the surface area of each prism using the information in the drawings and the height information that follows. Draw the net of each prism first.

- The triangular prism has a height of 10 cm.
- The hexagonal prism has a height of 5 cm.

- What does the perimeter of the base indicate about the lateral surface?
- What do all right prisms have in common in terms of describing the surface area?

Write a summary about finding the surface area of a right prism.

Check your summary.

- Do you describe how the perimeter of the base is related to the lateral surface of a prism?
- Do you explain the method for finding the surface area of a prism?
- Do you provide the formula for the surface area of a right prism, and explain what it means?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**One way I can figure out the surface area of a right prism is …**