# Lesson 14

Nets and Surface Area

### Lesson Narrative

Previously, students learned about polyhedra, analyzed and defined their features, and investigated their physical representations. Students also identified the polygons that compose a polyhedron; they recognized a net as an arrangement of these polygons and as a two-dimensional representation of a three-dimensional figure.

This lesson extends students' understanding of polyhedra and their nets. They practice visualizing the polyhedra that could be assembled from given nets and use nets to find the surface area of polyhedra.

### Learning Goals

Teacher Facing

• Match polyhedra with their nets and justify (orally) that they match.
• Use a net with gridlines to calculate the surface area of a prism or pyramid and explain (in writing) the solution method.
• Visualize and identify the polyhedron that can be assembled from a given net.

### Student Facing

Let’s use nets to find the surface area of polyhedra.

### Required Preparation

Prepare physical copies of the nets in the warm-up, in case needed to support students with visualization. The blackline master contains a larger version of these nets.

Make copies of the nets in the blackline master for the main activity. Prepare one set of 3 nets (A, B, and C) and some glue or tape for each group of 3 students.

### Student Facing

• I can match polyhedra to their nets and explain how I know.
• When given a net of a prism or a pyramid, I can calculate its surface area.

### Glossary Entries

• base (of a prism or pyramid)

The word base can also refer to a face of a polyhedron.

A prism has two identical bases that are parallel. A pyramid has one base.

A prism or pyramid is named for the shape of its base.

• face

Each flat side of a polyhedron is called a face. For example, a cube has 6 faces, and they are all squares.

• net

A net is a two-dimensional figure that can be folded to make a polyhedron.

Here is a net for a cube.

• polyhedron

A polyhedron is a closed, three-dimensional shape with flat sides. When we have more than one polyhedron, we call them polyhedra.

Here are some drawings of polyhedra.

• prism

A prism is a type of polyhedron that has two bases that are identical copies of each other. The bases are connected by rectangles or parallelograms.

Here are some drawings of prisms.

• pyramid

A pyramid is a type of polyhedron that has one base. All the other faces are triangles, and they all meet at a single vertex.

Here are some drawings of pyramids.

• surface area

The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps.

For example, if the faces of a cube each have an area of 9 cm2, then the surface area of the cube is $$6 \boldcdot 9$$, or 54 cm2.