Using Nets to Find Surface Area

3D shapes such as cubes, rectangular prisms, cylinders, and pyramids all have surface areas which can be measured and also calculated. The concept of surface area can be explained and illustrated using nets. Nets are a 2-dimensional representation of a 3-dimensional shape. Note: If you're looking for worksheets you'll find them here at the foot of this page.

animated image showing how a net can represent and cube

Explore nets with boxes and other everyday shapes with your children. You might mention that, in real life, boxes have overlapping edges to give them strength.

Nets

Below are a number of 3D shapes with corresponding nets:

Cubes

3D representation of a cube
2D net representing a cube

Rectangular Prisms

3D representation of a rectangular prism
2D net representing a rectangular prism

Triangular Prisms

3D representation of a triangular prism
2D net representing a triangular prism

Pyramids

3D representation of a pyramid
2D net representing a pyramid

Cylinders

3D representation of a cylinder
2D net representing a cylinder

Different Nets - and non-nets

Nets that form three-dimensional shapes can be configured in different ways. Look and the examples below and discuss which are nets of a cube and which are not. You can get some hands-on practice with the help of this print-out that can be cut up and folded to form a variety of 3D shapes. Some students will get most benefit from cutting and folding the pre-drawn nets while others will enjoy drawing their own nets first which can be done with the help of this printable graph paper generator.

Nets

Alternative correct net as a representation of a cube Alternative correct net as a representation of a cube Alternative correct net as a representation of a cube Alternative correct net as a representation of a cube

Not Nets

Alternative net as an incorrect representation of a cube Alternative net as an incorrect representation of a cube Alternative net as an incorrect representation of a cube Alternative net as an incorrect representation of a cube

From Nets to Surface Area

Once the concept of nets is understood, their use to help calculate surface area should become straightforward although many students will benefit from a recap of calculating area for 2D shapes.

Note: Students often confuse the concepts of area and volume. Be alert to this and provide some hands-on examples to help. For example, fill a bottle with water then wrap it in paper and in both cases discuss what is the volume and what is the surface area. Also, be sure that there are no language barriers that might inhibit students understanding. e.g. the term “surface” might not be properly understood.

Surface Area Using Nets: Examples

Work through the examples below with your children before practicing with the surface area worksheets that follow them.

Example - Rectangular Prism #1

3d image of rectangular prism with sides of 2,4, and 8
2d net of a rectangular prism

The net is made from 6 rectangles:

  • 8 x 2 = 16
  • 8 x 4 = 32
  • 8 x 2 = 16
  • 8 x 4 = 32
  • 2 x 4 = 8
  • 2 x 4 = 8
  • 16 + 32 + 16 + 32 + 8 + 8 = 112 square units

Discuss the calculation with your children and highlight, if required, that the opposite faces are equal in dimension and that this means the calculation can be simplified. e.g. [(8 x 2) + (8 x 4) + (2 x 4 )] x 2

Be aware that your children may not immediately identify all the required dimensions on the net. Help them to find "missing" dimensions from the ones given.

Example - Rectangular Prism #2

3d image of rectangular prism
2d net representing rectangualr prism

The net is made from 6 (2 x 3) rectangles. Opposite faces of the prism are equal.

  • (2 x 4) x 2 = 16
  • (4 x 3) x 2 = 24
  • (3 x 2) x 2 = 12
  • 16 + 24 + 12 = 52 square units

Example - Cube

3d image of a cube with sides measuring 6 linear units
2d net of cube

The net of a cube is made from 6 equally-sized squares

  • (4 x 4) x 6 = 96 square units

Example - Triangular Prism

3d triangular prism with 3-4-5 triangle and 7 units in length
2d net representing triangular prism

The net is made from 3 rectangles and 2 equally-sized triangles

  • 7 x 4 = 28
  • 7 x 3 = 21
  • 7 x 5 = 35
  • (3 x 4 ÷ 2) x 2 = 12
  • 28 + 21 + 35 + 12 = 96 square units

Nets and Surface Area Worksheets

The worksheets below include an initial hands-on activity with cut-out and fold instructions to show how nets can represented various 3D shapes and their surface areas.

All Geometry 24 Worksheets Terms/ Definitions Formulas/ Equations 2D Shapes 3D Shapes Quadrilaterals Measuring Angles Using a Protractor Adding and Subtracting Angles Angle Properties Finding Angles Symmetry Area Volume Surface Area Perimeter Coordinate System Coordinate Graphing Pythagoras' Theorem Distance Between Two Points Congruent Triangles Similar Triangles Transformations Dilations

 

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