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

6.G.A.4

6.G.4

6.G.A.4