In this lesson, students will cut out templates and make models of two square pyramids. They will take measurements and calculate the total surface area of each square pyramid. Students will compare the surface areas of two square pyramids and find the volume of each square pyramid and compare.

#### Objectives

- We will be able to measure accurately to the nearest tenth of a centimeter.
- We will be able to calculate the total surface area of a square pyramid.
- We will compare areas using ratios.
- We will calculate the total surface area of a truncated pyramid.
- We will be able to calculate the volume of a square pyramid.

**Prerequisite**

Students will need to know how to find the area of a triangle.

#### Assessment

- Surface Area of a Pyramid worksheet
- Small and large 3D pyramids
- Truncated Pyramid worksheet
- Challenge Activity worksheet

#### Time Required

1 hour

## Materials/Resources Needed

- Document camera/projector
- Art images (linked below in the activities)
- Activity pages (1
**–**4) - Centimeter Rulers
- Scissors
- Paper
- Pencil

## North Carolina Curriculum Alignment

## Activity One: Surface Area of a Pyramid

**NOTE:** *All pages referenced below are linked above in Materials/Resources Needed as “Activity pages.”*

- Provide students with the Surface Area of a Pyramid worksheet and the pyramid templates (activity pages 1
**–**2). Have students carefully cut out the two templates for pyramids and then fold along the lines and glue to form two square pyramids.*Note: When folding, it is important they use a straight edge and form sharp, accurate folds.* - Ask students to share any observations they have made about their two pyramids. They can compare/contrast them. In observing their own square pyramids, students should note the height of the smaller pyramid is one-half the height of the larger pyramid.
- Next, have the students measure the base and height of each pyramid.
- Then have students complete and record the calculations on the Surface Area of a Pyramid worksheet. Students should include explanations of how they made the calculations.

## Activity Two: Truncated Pyramid

- Project Sol Lewitt’s
*Untitled*. Ask students to share their observations about the artwork. Perhaps they will notice that this could be thought of as a pyramid with the top cut off. Such a figure is called a truncated pyramid. - Provide students with the Truncated Pyramid worksheet (activity page 3). Ask students to use their pyramids to solve questions #1-2. Go over answers together as a class or collect papers.
- Encourage or require students to complete the Challenge Activity worksheet (activity page 4). Students will find the volume of each pyramid. They could do research to find the formula for the volume of a pyramid. They will need to find the height of the pyramid. You may want to have a classroom discussion of the Pythagorean Theorem to help them see how to use the Pythagorean Theorem to determine the height.