1. Module 4

1.20. Page 3

Mathematics 10-3 Module 4 Lesson 4

Module 4: Area

 

Explore

 

You have just explored the net of a cube or rectangular prism, now you will explore the nets for other 3-D objects.

 

m10_3_trythis.jpg Try This

 

Go to “Exploring Surface Area, Volume, and Nets,” and try to identify the correct net for each 3-D object. Do not spend too much time on the cone and the cylinder. You will investigate the cone and the cylinder in the next lesson.

 

Now that you can form nets for 3-D objects, you will use nets to help find the surface area of 3-D objects.

 

m10_3_selfcheck.jpg Self-Check

 

Step 1: Print a copy of “Rectangular Prism.” Cut out the prism, fold it, and then tape this net to form a rectangular prism. The grid should be on the outside of the prism.

 

This illustration shows a net for a rectangular prism. The net has four rows. The top row consists of three rectangles—one measuring 6 units tall by 13 units wide with two rectangles 6 units tall and 4 units wide on the left and right side. The second row has one rectangle 4 units tall and 13 units wide directly below the large rectangle in the top row. The third row has one rectangle 6 units tall and 13 units wide directly below the large rectangle in the second row. The fourth row has one rectangle 4 units tall and 13 units wide directly below the large rectangle in the third row.

SC 1. Sketch of the rectangular prism you made, and show the prism’s dimensions.

 

SC 2. What are the areas of each face? Write the area on each face.

 

SC 3. What is the surface area of the prism based on the net?

 

Compare your answers.

 

You have just used a net to help find the surface area of a rectangular prism. A similar approach can be used to find the surface area of a pyramid.

 

This illustration shows a net for a pyramid with a square base measuring 8 units on a side and triangular sides with a height of 7 units.

Step 2: Print a copy of “Pyramid.” Cut out and tape your net together to form the prism.

 

m10_3_trythis.jpg Try This

 

TT 1. What is the area of each face?

 

TT 2. What is the total surface area of this pyramid?

 

m10_3_share.jpg Share

 

Choose either the rectangular prism calculations (SC 1 to SC 3) or the pyramid surface area calculations (TT 1 and TT 2) to work on during this Share.

 

Discuss the following questions with a partner or group.

  • What patterns did you notice when you were finding the surface area of each side of the prism?

  • What formula for surface area did you use for each side?

  • Did some sides have the same surface area as others?

  • How many sides were the same?

  • Could you develop a formula to find the surface area of a rectangular prism or pyramid so you did not have to use a net in the future?

Share your answers to these questions and any formulas (or attempts at formulas) with other groups. What are the similarities and differences between the formulas you each created for finding the surface area of a prism or pyramid?

 

Place a summary of your discussions and resulting formulas in your course folder for future reference.