Nets & Surface Area

What is a net?

A net is a 3D shape unfolded and laid flat. Picture a cardboard box cut along its edges and opened out. The flat shape you get is the net.

Fold it back up and every flat piece becomes one face of the box. A cube's net is six squares. A rectangular prism's net is six rectangles. A triangular prism's net is three rectangles and two triangles.

What is surface area?

Surface area is the total area of the outside of a shape. It is how much paper you would need to wrap it, with no overlap and no gaps.

Because a net is the surface laid flat, the surface area is just the sum of the areas on the net. You do not need a formula to understand it. You need to add up the pieces.

Adding up the pieces

Take a 4 by 3 by 2 box. Its net has six rectangles: two of 4 by 3, two of 4 by 2, and two of 3 by 2.

Their areas are 12, 12, 8, 8, 6, and 6. Add them up and you get 52. So the surface area is 52 square units.

The formula 2 × (l×w + l×h + w×h) is that same sum written in shorthand. If your kid can add the net, they already understand what the formula is doing.

What they're learning

• A net is a 3D shape unfolded flat, one piece for each face.
• Surface area is the sum of the areas of every face.
• The pieces do not change size when the net folds up.
• Counting the net gives the same answer as the formula.

Aliases

• Nets
• Surface area
• Unfolding 3D shapes
• Faces

Refresher

A net is a 3D shape cut along its edges and laid flat, one piece per face. Surface area is the total area of the outside, which is the sum of all the pieces on the net. The formula is just that sum in shorthand.

Try this together

Two or three minutes at the table is enough.

1. Open the module. The solid is a rectangular prism 4 by 3 by 2. Look at the flat net first.
2. Ask your kid to name each piece and its size before folding anything.
3. Drag the Fold slider. Point out that the pieces do not change size, they just stand up.
4. Set the solid to Cube with side 3. Ask how many squares are in the net and what each one's area is. Six squares of 9 gives 54.

The net always has the same number of pieces as the solid has faces. If a piece is missing, the surface area will come out too small.

Words you might hear

• Net: a 3D shape unfolded flat, with one piece per face.
• Face: one flat surface of a solid.
• Surface area: the total area of all the faces, measured in square units.

Your kid does not need to memorise the surface-area formulas. Counting the net gives the same answer and shows why the formula works.

Deeper dive

Take a 4 by 3 by 2 box. Unfold it and you get six rectangles: two that are 4 by 3, two that are 4 by 2, and two that are 3 by 2. Their areas are 12, 12, 8, 8, 6, and 6. Add them to get 52, so the surface area is 52 square units.

Folding the net up does not change any piece. The module's Fold slider just stands the flat pieces up.