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 three-dimensional 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.
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 \(8+8+6+6+12+12=52\).
- 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.
Each flat side of a polyhedron is called a face. For example, a cube has 6 faces, and they are all squares.
A net is a two-dimensional figure that can be folded to make a polyhedron.
Here is a net for a cube.
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.
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.
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.