# 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.  ## 14.2: Using Nets to Find Surface Area

Your teacher will give you the nets of three polyhedra to cut out and assemble. 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. 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 $8+8+6+6+12+12=52$.