Lesson 15

More Nets, More Surface Area

This lesson further develops students’ ability to visualize the relationship between nets and polyhedra and their capacity to reason about surface area.

Previously, students started with nets and visualized the polyhedra that could be assembled from the nets. Here they go in the other direction—from polyhedra to nets. They practice mentally unfolding three-dimensional shapes, drawing two-dimensional nets, and using them to calculate surface area. Students also have a chance to compare and contrast surface area and volume as measures of two distinct attributes of a three-dimensional figure.

Draw and assemble a net for the prism or pyramid shown in a given drawing.
Interpret (using words and other representations) two-dimensional representations of prisms and pyramids.
Use a net without gridlines to calculate the surface area of a prism or pyramid and explain (in writing) the solution method.

Let’s draw nets and find the surface area of polyhedra.

Copy and cut the blackline master for the Building Prisms and Pyramids activity. Make one copy for every 9 students, so that each student gets one drawing of a polyhedron. Consider assignments of polyhedra in advance.

I can calculate the surface area of prisms and pyramids.
I can draw the nets of prisms and pyramids.

Building On

5.MD.C.5

Addressing

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.