Lesson 14: Nets and Surface Area

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

14.1: Matching Nets

Each of the following 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.

Five nets of polyhedra labeled 1--5.
 
Five polyhedra labeled A--E.

14.2: Using Nets to Find Surface Area

Your teacher will give you the nets of three polyhedra to cut out and assemble.

Three nets on a grid, labeled A, B, and C. Net A is composed of two rectangles that are 5 units tall by 6 units wide, two that are 5 units high and one unit wide, and two that are one unit high and six units wide. Net B is a square with a side length of 4 units and is surrounded by triangles that are four units wide at the base and four units high. Net C is a square with a side length of 3, a rectangle 3 units wide and 5 units high, another rectangle that is 3 units wide and 4 units tall, and two triangles, one on either side, that are three units tall by four units across.

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

    A:

    B:

    C:

  2. Cut out your nets and use them to create three-dimensional shapes.

  3. Find the surface area of each polyhedron. Explain your reasoning clearly.

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.

The net for this pentagonal pyramid is a pentagon surrounded by triangles on each side.

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.

The net for this pentagonal prism is a pentagon surrounded by rectangles on each side with an additional pentagon attached to the opposite side of one of the rectangles.

In a rectangular prism, there are three pairs of parallel and identical rectangles. Any pair of these identical rectangles can be the bases.

Three images of a rectangular prism. Each image has one set of opposing sides of the polyhedron shaded and labeled “base."
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.

A polyhedron made up of six rectangles. Two rectangles are 8 square units in area, 2 are 6 square units, and 2 are 12 square units.

The surface area of the rectangular prism is 52 square units because $8+8+6+6+12+12=52$.

Practice Problems ▶

Glossary

surface area

surface area

The surface area (in square units) is the number of unit squares it takes to cover all the surfaces of a three-dimensional figure without gaps or overlaps.