Cuboid Nets: Shapes, How Many, and How to Recognise Them

A cuboid net is an arrangement of six rectangles that folds into a cuboid, made of three pairs of equal faces. There are 11 net patterns, the same as for a cube. The topic is taught in Year 5.

Features of a Cuboid Net

A cuboid net always has 6 rectangles, and opposite faces of the cuboid are exactly the same size. Unlike a cube net, a cuboid uses three different sizes: length × width (base and top), length × height (front and back), width × height (left and right).

How Many Cuboid Nets Are There?

There are 11 patterns, identical to the cube: six 1-4-1, three 2-3-1, one 2-2-2 and one 3-3.

How to Check a Cuboid Net

1. Count exactly six rectangles.
2. Find exactly three matching pairs of sizes.
3. Make sure there is no 2×2 block and no five faces in a straight row.

Drawing a Net and Surface Area

For a 6 × 4 × 3 cm cuboid, draw four walls in a row (6×3, 4×3, 6×3, 4×3), a 6×4 base below one 6×3 wall and a 6×4 top above the opposite one. Surface area = 2 × (24 + 18 + 12) = 108 cm² and volume = 72 cm³.

Worked Examples

• Net of 2 rectangles each of 8×5, 8×3, 5×3 cm: surface area = 2 × (40 + 24 + 15) = 158 cm².
• Three 6×2 and three 6×4 rectangles cannot fold into a cuboid, because the sizes do not form three pairs.
• A 10×5×4 cm gift box needs 2 × (50 + 40 + 20) = 220 cm² of wrapping paper.

Summary

Six rectangles, three pairs, 11 patterns. Algonova has helped more than 1,000,000 students in 97 countries; a free maths diagnostic of about 60 minutes shows where your child stands.