Nets and Surface Area

Warmup

Activity #1

 Explore Nets of a Prism and a Cube.

In geometry, a net of a polyhedron is an arrangement of non-overlapping edge -joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. Not all polygons have a net. In this activity, you are going to see how the net structure of a prism and a cube look like.

RIGHT PRISM

• Move the slider up and down to see how the faces of a right prism are folded along the edges to form the prism.​

• Answer the questions below.

CUBE

• Drag the squares to form nets of a cube.​ See example on the left.

• Answer the questions below.

Activity #2

Match a Net to its Polygon.

Each of the nets below can be assembled into a polyhedron. In the exercise, you’ll be required to match a polygon to its net.

• Match each net with its corresponding polyhedron, and name the polyhedron.
• Explain how you know the net and polyhedron go together.

• Answer the questions below.

(1.) Name each polyhedron above.

(2.) Explain how you know each net and polyhedron go together.

The applet below has three nets that would form different polyhedra.

• Observe each net closely and note the different polygons involved.

• Answer the questions below.

(1.) Name the polyhedron that each net would form when assembled.

(2.) Find the surface area of each polyhedron.

(3.) Explain how you found the surface area of each polyhedron. Use the applet below if you need help. (Just click on the double arrow and move the slider.)

Activity #3

Practice on Exercise Questions Involving Nets and Polygons.

• Study the net below and note what polygon that makes up the faces.

• Answer the questions below about this net structure.

(1.) how many different types of polygons can be identified?

(2.) Can this net be assembled into a cube?

(3.) Explain how you know. Label parts of the net with letters or numbers if it helps your explanation.

Here below are two nets. Mai said that both nets can be assembled into the same triangular prism.

• Study the two nets and answer the questions that follow.

(1.) Do you agree?

(2.) Explain or show your reasoning.

• Answer the questions below to demonstrate your understanding of Net Structure.

Challenge #1

Challenge #2

Which of the following nets can be assembled into a rectangular prism.

Challenge #3

For each net below, decide if it can be folded into a triangular prism.