Nets of 3D shapes and surface area of a prism
Maths · Key Stage 3 · The School
What a net is
A NET is a 2D shape that folds up into a 3D solid. A cube's net is six squares arranged so that folding along the joins brings all six faces together with no gaps or overlaps. The same solid can have more than one correct net — a cube has eleven different nets that all work.
Matching faces to solids
A triangular prism's net has two triangles (the ends) and three rectangles (the sides), arranged so each rectangle's edge matches the triangle edge it will join. A cylinder's net is two circles plus one rectangle, where the rectangle's width must exactly equal the circle's circumference — otherwise the curved side will not close up properly.
Using a net to find surface area
The net shows every face laid flat, so SURFACE AREA is simply the total area of every face in the net, added together. This is often easier than trying to picture the solid in 3D — each flat face is an ordinary 2D shape you already know how to find the area of.
A cuboid measures 5cm by 3cm by 2cm. It has three PAIRS of matching faces: two faces of 5 × 3 = 15 cm² each, two faces of 5 × 2 = 10 cm² each, and two faces of 3 × 2 = 6 cm² each. Total surface area = (2 × 15) + (2 × 10) + (2 × 6) = 30 + 20 + 12 = 62 cm². Drawing the net first, all six rectangles laid flat, makes it far harder to forget one of the six faces than trying to picture the solid from the outside.