Nets and Surface Area

Student 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.

Pentagonal pyramid

Net for pentagonal pyramid. 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.

pentagonal prism

Net for 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=528+8+6+6+12+12=52.

Visual / Anchor Chart

Standards

Addressing
6.G.4

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.