Lesson 14
Nets and Surface Area
Let’s use nets to find the surface area of polyhedra.
14.1: Matching Nets
Each of the nets can be assembled into a polyhedron. Match each net with its corresponding polyhedron, and name the polyhedron. Be prepared to explain how you know the net and polyhedron go together.
14.2: Using Nets to Find Surface Area

Name the polyhedron that each net would form when assembled.
 Your teacher will give you the nets of three polyhedra. Cut out the nets and assemble the threedimensional shapes.
 Find the surface area of each polyhedron. Explain your reasoning clearly.

For each net, decide if it can be assembled into a rectangular prism.

For each net, decide if it can be folded into a triangular prism.
Summary
A net of a pyramid has one polygon that is the base. The rest of the polygons are triangles. A pentagonal pyramid and its net are shown here.
A net of a prism has two copies of the polygon that is the base. The rest of the polygons are rectangles. A pentagonal prism and its net are shown here.
In a rectangular prism, there are three pairs of parallel and identical rectangles. Any pair of these identical rectangles can be the bases.
Because a net shows all the faces of a polyhedron, we can use it to find its surface area. For instance, the net of a rectangular prism shows three pairs of rectangles: 4 units by 2 units, 3 units by 2 units, and 4 units by 3 units.
The surface area of the rectangular prism is 52 square units because \(8+8+6+6+12+12=52\).
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 twodimensional figure that can be folded to make a polyhedron.
Here is a net for a cube.
 polyhedron
A polyhedron is a closed, threedimensional 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 cm^{2}, then the surface area of the cube is \(6 \boldcdot 9\), or 54 cm^{2}.