Nets & Surface Area
Watch a net fold into a 3D shape and see how its surface area adds up, face by face.
Dimensions
Units
Surface area, face by face
Drag the shape to turn it. Slide to fold one face at a time.
How to use the nets and surface area tool
- Pick a shape — cube, rectangular prism, triangular prism or square pyramid.
- Set the dimensions with the sliders or by typing, and choose your units.
- Press Fold it and watch the net fold up into the solid, one face at a time. Drag the slider to fold it slowly, or drag the shape to turn it around.
- Read the surface area face by face in the table. Matching faces share a color in the net and in the table, so you can see which faces are the same size.
- Print the net to cut out and fold into a real 3D shape.
What is a net?
A net is a flat shape that folds up into a 3D solid. If you carefully unfold a cereal box and lay it flat, what you are holding is its net. A cube’s net is six squares, often drawn as a cross; a square pyramid’s net is a square with a triangle on each side.
Most solids have more than one net — a cube has 11 different ones. The tool shows the net that is easiest to picture folding, with the base in the middle.
What is surface area?
Surface area is the total area of all the faces of a 3D shape — how much paper you would need to cover it with no gaps and no overlaps. It is measured in square units, such as cm² or in².
Nets make surface area easy to understand: unfold the shape, find the area of each flat face, and add them up. That is exactly what the table in the tool does, and it is how surface area is taught in grade 6 (Common Core standard 6.G.4).
Surface area formulas, with examples
Rectangular prism
SA = 2(lw + lh + wh)
A rectangular prism has three pairs of matching faces: top and bottom, front and back, left and right. Work out one of each pair, add them, and double it. For a box 8 cm long, 5 cm wide and 4 cm high: 2(8×5 + 8×4 + 5×4) = 2(40 + 32 + 20) = 184 cm².
Cube
SA = 6s²
All six faces of a cube are the same square. For a cube with 5 cm sides: 6 × 5² = 6 × 25 = 150 cm².
Triangular prism
SA = bh + l(b + 2s)
Two triangles (together b × h) plus three rectangles that wrap around the length. For an isosceles triangle with base b = 6 cm and height h = 4 cm, each sloping side is s = √(4² + 3²) = 5 cm. With a length of 9 cm: 6×4 + 9 × (6 + 10) = 24 + 144 = 168 cm².
Square pyramid
SA = a² + 2aℓ
One square base plus four triangles. The triangles use the slant height ℓ — the height up the middle of a triangle, not the height of the pyramid. For a base of 6 cm and a height of 5 cm: ℓ = √(5² + 3²) ≈ 5.83 cm, so SA = 36 + 2 × 6 × 5.83 ≈ 105.97 cm².
Surface area or volume?
Surface area is the outside of a shape; volume is the space inside it. Surface area is in square units, volume in cubic units. The 8 × 5 × 4 box above has a surface area of 184 cm² and a volume of 8 × 5 × 4 = 160 cm³. The tool shows both, so students can see that two boxes with the same volume can have different surface areas.
Ideas for the classroom
- Predict, then fold. Show the flat net and ask students to name the solid before pressing Fold it.
- Which faces match? Before looking at the table, have students list the faces that must be the same size, then check the colors.
- Build it. Print nets on card stock, cut them out and fold them. Measuring the paper faces with a ruler and adding up the areas is surface area students can hold.
- Same volume, different wrap. Try 8 × 5 × 4 and 10 × 4 × 4 (both 160 cm³) and compare the surface areas.
- Slant height versus height. Change the pyramid’s height and watch the slant height and the surface area change with it.
Frequently asked questions
How do you find surface area using a net?
Draw or unfold the net, find the area of each face (length × width for rectangles, ½ × base × height for triangles), then add all the areas together.
Why is the slant height used for a pyramid?
Each triangle’s area needs the height of that triangle, which runs up its face at an angle. The pyramid’s height is measured straight up through the middle, so it is shorter than the slant height.
Can I print the net?
Yes. Print net prints the net for your dimensions on one page, with a solid line to cut on and dashed lines to fold on. Leave small tabs of paper when you cut if you want to glue it together.
Is the tool free?
Yes — free, no sign-up, and it works on phones, tablets and computers.